Empirical for n mod 6 = 0: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (765148247/296987937523200)*n^12 + (3607479779/74246984380800)*n^11 + (16953596969/21999106483200)*n^10 + (4349872181/428554022400)*n^9 + (4187791683923/38131784570880)*n^8 + (22581885121097/23832365356800)*n^7 + (2632261949431/407390860800)*n^6 + (100828838088581/2648040595200)*n^5 + (90580505842/500987025)*n^4 + (776585786833/1526817600)*n^3 + (367133314727/805820400)*n^2 + (15888094529/6466460)*n + 13015 for n>8
Empirical for n mod 6 = 1: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (61977430807/24056022939379200)*n^12 + (292212191303/6014005734844800)*n^11 + (7416161042327/9622409175751680)*n^10 + (9514786023727/937247646988800)*n^9 + (9166497339989713/83394212856514560)*n^8 + (49491707379262963/52121383035321600)*n^7 + (156565065616348327/24056022939379200)*n^6 + (221966926475157307/5791264781702400)*n^5 + (166587721042028141/946649050855200)*n^4 + (3317108392881008249/7302721249454400)*n^3 + (12364260106576242419/34687925934908400)*n^2 + (32264294394021054229/22547151857690460)*n + (250027823774333/669462604992) for n>8
Empirical for n mod 6 = 2: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (1878090607/728970392102400)*n^12 + (292207099279/6014005734844800)*n^11 + (7415621011759/9622409175751680)*n^10 + (9513635449967/937247646988800)*n^9 + (45768322538735413/416971064282572800)*n^8 + (49336767392877779/52121383035321600)*n^7 + (154691146756364387/24056022939379200)*n^6 + (658195919314684081/17373794345107200)*n^5 + (177583343352686713/1135978861026240)*n^4 + (300050947558960853/811413472161600)*n^3 + (140480050256943664/197090488266525)*n^2 + (35680355541276970453/22547151857690460)*n + (121196115574268/10460353203) for n>8
Empirical for n mod 6 = 3: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (765148247/296987937523200)*n^12 + (3607479779/74246984380800)*n^11 + (16953596969/21999106483200)*n^10 + (4349872181/428554022400)*n^9 + (4187791683923/38131784570880)*n^8 + (22581885121097/23832365356800)*n^7 + (2632261949431/407390860800)*n^6 + (100828838088581/2648040595200)*n^5 + (90580505842/500987025)*n^4 + (776585786833/1526817600)*n^3 + (367133314727/805820400)*n^2 + (15888094529/6466460)*n - (75249/64) for n>8
Empirical for n mod 6 = 4: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (61977430807/24056022939379200)*n^12 + (292212191303/6014005734844800)*n^11 + (7416161042327/9622409175751680)*n^10 + (9514786023727/937247646988800)*n^9 + (9166497339989713/83394212856514560)*n^8 + (49491707379262963/52121383035321600)*n^7 + (156565065616348327/24056022939379200)*n^6 + (221966926475157307/5791264781702400)*n^5 + (166587721042028141/946649050855200)*n^4 + (3317108392881008249/7302721249454400)*n^3 + (12364260106576242419/34687925934908400)*n^2 + (32264294394021054229/22547151857690460)*n + (152347105404965/10460353203) for n>8
Empirical for n mod 6 = 5: a(n) = (1/40404496128981304320)*n^20 + (1/183656800586278656)*n^19 + (313/490742867963335680)*n^18 + (17503/354425404640186880)*n^17 + (89641/32074697252505600)*n^16 + (4163/34365747056256)*n^15 + (5533657/1336445718854400)*n^14 + (989078033/8686897172553600)*n^13 + (1878090607/728970392102400)*n^12 + (292207099279/6014005734844800)*n^11 + (7415621011759/9622409175751680)*n^10 + (9513635449967/937247646988800)*n^9 + (45768322538735413/416971064282572800)*n^8 + (49336767392877779/52121383035321600)*n^7 + (154691146756364387/24056022939379200)*n^6 + (658195919314684081/17373794345107200)*n^5 + (177583343352686713/1135978861026240)*n^4 + (300050947558960853/811413472161600)*n^3 + (140480050256943664/197090488266525)*n^2 + (35680355541276970453/22547151857690460)*n - (1743635525390275/669462604992) for n>8