Empirical for n mod 6 = 0: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (1574392516666993/10810360925844480000)*n^11 + (978739148259073/360345364194816000)*n^10 + (24571139689687663/600575606991360000)*n^9 + (5300542253011/9119527560000)*n^8 + (20200512292873039/2893930079040000)*n^7 + (3068780283294527/42203146986000)*n^6 + (7335822803151135379/13607317694880000)*n^5 + (1198673088973761787/566971570620000)*n^4 + (12153252237024822829/304904711311200)*n^3 - (341732194129197383/2419878661200)*n^2 + (124926279100165/803134332)*n + 3581971 for n>14
Empirical for n mod 6 = 1: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (382577381000220899/2626917704980208640000)*n^11 + (237833610408018419/87563923499340288000)*n^10 + (53737141007933056981/1313458852490104320000)*n^9 + (243440103808657447/418832542248120000)*n^8 + (56793469675395285541/8137317963677760000)*n^7 + (15092596177653034039/207671135531359500)*n^6 + (326136238183204681955897/602623876923726840000)*n^5 + (79576486888092107832899/37663992307732927500)*n^4 + (12828209354164838733315299/324077729367870878400)*n^3 - (4919596366649209767105667/34722613860843308400)*n^2 + (228171364474541373849247/1555753478180641740)*n + (60744770252595605/41841412812) for n>14
Empirical for n mod 6 = 2: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (14169532639810937/97293248332600320000)*n^11 + (713500832970760217/262691770498020864000)*n^10 + (53737039848504686981/1313458852490104320000)*n^9 + (243437784696504947/418832542248120000)*n^8 + (397617086905499425637/56961225745744320000)*n^7 + (241598774557066231289/3322738168501752000)*n^6 + (1298911319920695358577213/2410495507694907360000)*n^5 + (629761544758392905085067/301311938461863420000)*n^4 + (6482555351926042554042419/162038864683935439200)*n^3 - (14700880279858079362739933/104167841582529925200)*n^2 + (6715961875618969240429/51858449272688058)*n + (38665078940709440/10460353203) for n>14
Empirical for n mod 6 = 3: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (1574392516666993/10810360925844480000)*n^11 + (978739148259073/360345364194816000)*n^10 + (24571139689687663/600575606991360000)*n^9 + (5300542253011/9119527560000)*n^8 + (20200512292873039/2893930079040000)*n^7 + (3068780283294527/42203146986000)*n^6 + (7335822803151135379/13607317694880000)*n^5 + (1198673088973761787/566971570620000)*n^4 + (12153252237024822829/304904711311200)*n^3 - (341732194129197383/2419878661200)*n^2 + (124926279100165/803134332)*n + (5249715/4) for n>14
Empirical for n mod 6 = 4: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (382577381000220899/2626917704980208640000)*n^11 + (237833610408018419/87563923499340288000)*n^10 + (53737141007933056981/1313458852490104320000)*n^9 + (243440103808657447/418832542248120000)*n^8 + (56793469675395285541/8137317963677760000)*n^7 + (15092596177653034039/207671135531359500)*n^6 + (326136238183204681955897/602623876923726840000)*n^5 + (79576486888092107832899/37663992307732927500)*n^4 + (12828209354164838733315299/324077729367870878400)*n^3 - (4919596366649209767105667/34722613860843308400)*n^2 + (228171364474541373849247/1555753478180641740)*n + (38926406107280228/10460353203) for n>14
Empirical for n mod 6 = 5: a(n) = (1/214669087933277669852160000)*n^23 + (1/466671930289734064896000)*n^22 + (1/2142662673506584320000)*n^21 + (5743/60606744193471956480000)*n^20 + (246703/17316212626706273280000)*n^19 + (183683/127593145670467276800)*n^18 + (2264102497/22328800492331773440000)*n^17 + (3614440891/656729426245052160000)*n^16 + (19373516273/79603566817582080000)*n^15 + (835401743/94766150973312000)*n^14 + (353289165959/1365083841401280000)*n^13 + (12883366240487/1960120387653120000)*n^12 + (14169532639810937/97293248332600320000)*n^11 + (713500832970760217/262691770498020864000)*n^10 + (53737039848504686981/1313458852490104320000)*n^9 + (243437784696504947/418832542248120000)*n^8 + (397617086905499425637/56961225745744320000)*n^7 + (241598774557066231289/3322738168501752000)*n^6 + (1298911319920695358577213/2410495507694907360000)*n^5 + (629761544758392905085067/301311938461863420000)*n^4 + (6482555351926042554042419/162038864683935439200)*n^3 - (14700880279858079362739933/104167841582529925200)*n^2 + (6715961875618969240429/51858449272688058)*n + (59699461586312453/41841412812) for n>14