cp's OEIS Frontend

a(n) = n^2*(n^10-135n^8+8005n^6-262665n^4+4816354n^2-39858840)/720, n>=13.

G.f.: 4*x^4*(240*x^21-3120*x^20+20470*x^19-105106*x^18+512024*x^17-2216597*x^16+7650408*x^15-20251702*x^14+41149629*x^13-64905350*x^12+80399423*x^11-78967736*x^10+61875645*x^9-38631940*x^8+19002633*x^7-7392461*x^6+2560624*x^5-840251*x^4-8486*x^3-14835*x^2+182*x-14)/(x-1)^13. - Vaclav Kotesovec, Mar 25 2010

Explicit formula: a(n) = n*(n^9-90n^7+120n^6+3395n^5-8160n^4-62130n^3+204000n^2+463464n-1888080)/120, n>=10. For any fixed value of k > 1, a(n) = n^(2k)/k! - 9n^(2k-2)/2/(k-2)! + 6n^(2k-3)/(k-2)! + ... [Vaclav Kotesovec, Jan 31 2010]

G.f.: -x^4*(468*x^16-7964*x^15+57164*x^14-238936*x^13+664383*x^12-1323653*x^11+1986964*x^10-2334676*x^9+2209082*x^8-1718662*x^7+1118210*x^6-595746*x^5+216519*x^4-38229*x^3+34186*x^2+922*x+208)/(x-1)^11. [Vaclav Kotesovec, Mar 25 2010]

Explicit formula: a(n) = n^2*(n^12-189n^10+16135n^8-801255n^6+24595984n^4-445931556n^2+3756080880)/5040, n>=14. For any fixed value of k > 1, a(n) = n^(2k)/k! - 9n^(2k-2)/2/(k-2)! + (243k+143)*n^(2k-4)/24/(k-3)! - ...

G.f.: -4*x^4 * (2535*x^24 -61497*x^23 +627330*x^22 -3849410*x^21 +16791330*x^20 -58053150*x^19 +170691269*x^18 -438580125*x^17 +976505385*x^16 -1844050487*x^15 +2900976825*x^14 -3760563305*x^13 +3991133690*x^12 -3450574470*x^11 +2418714751*x^10 -1370750375*x^9 +628081926*x^8 -228075638*x^7 +56855445*x^6 -6423333*x^5 +4868490*x^4 +36682*x^3 +20508*x^2 -60*x +4) / (x-1)^15. [Vaclav Kotesovec, Mar 25 2010]