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A253637 Second partial sums of ninth powers (A001017). 3
1, 514, 20710, 303050, 2538515, 14851676, 67518444, 254402940, 828707925, 2403012910, 6335265586, 15427298614, 35123831015, 75481410200, 154282348760, 301802764056, 567911055849, 1032378638010, 1819533917950, 3118689197890, 5212124524411, 8512829068724, 13614686274500, 21358351020500, 32916713032125, 49904578722726 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The formula for the second partial sums of m-th powers is: b(n,m) = (n+1)*F(m) - F(m+1), where F(m) are the m-th Faulhaber's formulas.

LINKS

Table of n, a(n) for n=1..26.

Luciano Ancora, Recurrence relation for the second partial sums of m-th powers

Luciano Ancora, Second partial sums of the m-th powers

FORMULA

a(n) = n*(n+1)*(n+2)*(n^2+n-1)*(n^2+3n+1)*(6*n^4+24*n^3+5*n^2-38*n+25)/660.

a(n) = 2*a(n-1)-a(n-2)+n^9.

G.f.: x*(1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(1-x)^12. - Vincenzo Librandi, Jan 19 2015

MATHEMATICA

CoefficientList[Series[(1 + 502 x + 14608 x^2 + 88234 x^3 + 156190 x^4 + 88234 x^5 + 14608 x^6 + 502 x^7 + x^8)/(1-x)^12, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 19 2015 *)

PROG

(PARI) a(n) = (6*n^11 + 66*n^10 + 275*n^9 + 495*n^8 + 198*n^7 - 462*n^6 - 330*n^5 + 330*n^4 + 231*n^3 - 99*n^2 - 50*n)/660; \\ Michel Marcus, Jan 08 2015

CROSSREFS

Sequence in context: A045054 A301547 A229331 * A231415 A271760 A228999

Adjacent sequences:  A253634 A253635 A253636 * A253638 A253639 A253640

KEYWORD

nonn

AUTHOR

Luciano Ancora, Jan 07 2015

STATUS

approved

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Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)