Empirical for n mod 6 = 0: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (4103344021439/980060193826560000)*n^12 + (139892896141/1484939687616000)*n^11 + (330002517571873/180172682097408000)*n^10 + (306713018669401/10009593449856000)*n^9 + (1433867757096023/3574854803520000)*n^8 + (59070631175593/14895228348000)*n^7 + (12353483868558383/337625175888000)*n^6 + (244832685742859/662010148800)*n^5 + (603429253270296107/307984556880000)*n^4 + (5738773856103713/741139308000)*n^3 - (2196030992626501/94897202400)*n^2 + (14973543692203/349188840)*n + 1114571 for n>12
Empirical for n mod 6 = 1: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (332370865798159/79384875699951360000)*n^12 + (3090361257173/32803667644608000)*n^11 + (240571835971916777/131345885249010432000)*n^10 + (6037032181241957083/197018827873515648000)*n^9 + (1045292927089738667/2606069151766080000)*n^8 + (290683087812732751/73295694893421000)*n^7 + (121506912731550784187/3322738168501752000)*n^6 + (133764004906681537/361954048856400)*n^5 + (12964488369776468484460411/6628862646160995240000)*n^4 + (862402672883677110587/98467953745707000)*n^3 - (152841791737257137718481/6127520093089995600)*n^2 + (637065856344844038358/16910363893267845)*n + (50990443431946627/125524238436) for n>12
Empirical for n mod 6 = 2: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (4103344021439/980060193826560000)*n^12 + (33993973781303/360840344090688000)*n^11 + (240571832973481337/131345885249010432000)*n^10 + (6037031725857027083/197018827873515648000)*n^9 + (348429054388557589/868689717255360000)*n^8 + (1162695365674077779/293182779573684000)*n^7 + (243156022525984978909/6645476337003504000)*n^6 + (1607022854908168349/4343448586276800)*n^5 + (25163330315947619977508147/13257725292321990480000)*n^4 + (22673770184693337777707/3544846334845452000)*n^3 - (225706357762343437354931/12255040186179991200)*n^2 + (332292003996862436453/12298446467831160)*n + (36010454587845859/31381059609) for n>12
Empirical for n mod 6 = 3: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (4103344021439/980060193826560000)*n^12 + (139892896141/1484939687616000)*n^11 + (330002517571873/180172682097408000)*n^10 + (306713018669401/10009593449856000)*n^9 + (1433867757096023/3574854803520000)*n^8 + (59070631175593/14895228348000)*n^7 + (12353483868558383/337625175888000)*n^6 + (244832685742859/662010148800)*n^5 + (603429253270296107/307984556880000)*n^4 + (5738773856103713/741139308000)*n^3 - (2196030992626501/94897202400)*n^2 + (14973543692203/349188840)*n + (1632523/4) for n>12
Empirical for n mod 6 = 4: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (332370865798159/79384875699951360000)*n^12 + (3090361257173/32803667644608000)*n^11 + (240571835971916777/131345885249010432000)*n^10 + (6037032181241957083/197018827873515648000)*n^9 + (1045292927089738667/2606069151766080000)*n^8 + (290683087812732751/73295694893421000)*n^7 + (121506912731550784187/3322738168501752000)*n^6 + (133764004906681537/361954048856400)*n^5 + (12964488369776468484460411/6628862646160995240000)*n^4 + (862402672883677110587/98467953745707000)*n^3 - (152841791737257137718481/6127520093089995600)*n^2 + (637065856344844038358/16910363893267845)*n + (34916454453433519/31381059609) for n>12
Empirical for n mod 6 = 5: a(n) = (1/466671930289734064896000)*n^22 + (1/1247785909865599104000)*n^21 + (613/4329053156676568320000)*n^20 + (467/29709188330133312000)*n^19 + (70943/56291093678147328000)*n^18 + (1394917/17721270232009344000)*n^17 + (1301313047/328364713122526080000)*n^16 + (295963211/1824248406236256000)*n^15 + (11497053509/2084855321412864000)*n^14 + (5106462623/31588716991104000)*n^13 + (4103344021439/980060193826560000)*n^12 + (33993973781303/360840344090688000)*n^11 + (240571832973481337/131345885249010432000)*n^10 + (6037031725857027083/197018827873515648000)*n^9 + (348429054388557589/868689717255360000)*n^8 + (1162695365674077779/293182779573684000)*n^7 + (243156022525984978909/6645476337003504000)*n^6 + (1607022854908168349/4343448586276800)*n^5 + (25163330315947619977508147/13257725292321990480000)*n^4 + (22673770184693337777707/3544846334845452000)*n^3 - (225706357762343437354931/12255040186179991200)*n^2 + (332292003996862436453/12298446467831160)*n + (55366443969595987/125524238436) for n>12