Empirical for n mod 6 = 0: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (741964271/1378872567072000)*n^13 + (63231143/4821232752000)*n^12 + (8276006707/30936243492000)*n^11 + (735765311/171868019400)*n^10 + (130687254081983/2502398362464000)*n^9 + (29537035840267/59580913392000)*n^8 + (6209625523/1653372000)*n^7 + (670899741821/23643219600)*n^6 + (427076508509431/1705177656000)*n^5 + (2410384098141263/3126159036000)*n^4 + (97884488213414921/69296525298000)*n^3 + (163533714689/65356200)*n^2 + (17066258992/6235515)*n + 313559 for n>10
Empirical for n mod 6 = 1: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (60099106271/111688677932832000)*n^13 + (169016852759/12887155146096000)*n^12 + (182824902731/683409742596000)*n^11 + (1206858327721/281906518820850)*n^10 + (857663848044673783/16418235656126304000)*n^9 + (64683680554578769/130303457588304000)*n^8 + (367994725979087/97629963228000)*n^7 + (13269098693878141/465369491386800)*n^6 + (8427047247711292903/33563011803048000)*n^5 + (1251333984403482070153/1661369084250876000)*n^4 + (75735291797797667214313/41430391538506220250)*n^3 + (28694590306044551591/23210303382916650)*n^2 + (150614704958777026969/33820727786535690)*n + (3911555505770221/41841412812) for n>10
Empirical for n mod 6 = 2: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (741964271/1378872567072000)*n^13 + (169016846839/12887155146096000)*n^12 + (2011067337161/7517507168556000)*n^11 + (4827336062117/1127626075283400)*n^10 + (856988122268228063/16418235656126304000)*n^9 + (64460061521701529/130303457588304000)*n^8 + (365283782467267/97629963228000)*n^7 + (4387104495334313/155123163795600)*n^6 + (8387806765636223173/33563011803048000)*n^5 + (388401106187867746661/553789694750292000)*n^4 + (80496408349660477909169/331443132308049762000)*n^3 + (662975533129585364771/92841213531666600)*n^2 - (13743103420318983043/3074611616957790)*n + (3318210888598075/10460353203) for n>10
Empirical for n mod 6 = 3: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (741964271/1378872567072000)*n^13 + (63231143/4821232752000)*n^12 + (8276006707/30936243492000)*n^11 + (735765311/171868019400)*n^10 + (130687254081983/2502398362464000)*n^9 + (29537035840267/59580913392000)*n^8 + (6209625523/1653372000)*n^7 + (670899741821/23643219600)*n^6 + (427076508509431/1705177656000)*n^5 + (2410384098141263/3126159036000)*n^4 + (97884488213414921/69296525298000)*n^3 + (163533714689/65356200)*n^2 + (17066258992/6235515)*n + (413347/4) for n>10
Empirical for n mod 6 = 4: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (60099106271/111688677932832000)*n^13 + (169016852759/12887155146096000)*n^12 + (182824902731/683409742596000)*n^11 + (1206858327721/281906518820850)*n^10 + (857663848044673783/16418235656126304000)*n^9 + (64683680554578769/130303457588304000)*n^8 + (367994725979087/97629963228000)*n^7 + (13269098693878141/465369491386800)*n^6 + (8427047247711292903/33563011803048000)*n^5 + (1251333984403482070153/1661369084250876000)*n^4 + (75735291797797667214313/41430391538506220250)*n^3 + (28694590306044551591/23210303382916650)*n^2 + (150614704958777026969/33820727786535690)*n + (3176887862571922/10460353203) for n>10
Empirical for n mod 6 = 5: a(n) = (1/1060618023385759238400)*n^21 + (1/3607544297230473600)*n^20 + (1/26015944451181300)*n^19 + (1/299166101605800)*n^18 + (86269/402756141636576000)*n^17 + (4428089/390910372764912000)*n^16 + (1747621/3455015920902000)*n^15 + (19980437/1085862146569200)*n^14 + (741964271/1378872567072000)*n^13 + (169016846839/12887155146096000)*n^12 + (2011067337161/7517507168556000)*n^11 + (4827336062117/1127626075283400)*n^10 + (856988122268228063/16418235656126304000)*n^9 + (64460061521701529/130303457588304000)*n^8 + (365283782467267/97629963228000)*n^7 + (4387104495334313/155123163795600)*n^6 + (8387806765636223173/33563011803048000)*n^5 + (388401106187867746661/553789694750292000)*n^4 + (80496408349660477909169/331443132308049762000)*n^3 + (662975533129585364771/92841213531666600)*n^2 - (13743103420318983043/3074611616957790)*n + (4476847609874833/41841412812) for n>10