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A253710 Second partial sums of tenth powers (A008454). 1
1, 1026, 61100, 1169750, 12044025, 83384476, 437200176, 1864757700, 6779099625, 21693441550, 62545208076, 165314338826, 405941961425, 935824239000, 2042356907200, 4248401203176, 8470439399601, 16262944822650, 30186516503500, 54350088184350, 95193540843401, 162596916293876, 271426802958000, 443660070587500 (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..24.

Luciano Ancora, Recurrence relation

Luciano Ancora, Second partial sums of m-th powers

FORMULA

a(n) = n*(n+1)^2*(n+2)*(n^2 + 2*n - 2)*(2*n^6 + 12*n^5 + 16*n^4 - 16*n^3 - 17*n^2 + 30*n - 5)/264.

a(n) = 2*a(n-1)-a(n-2)+n^10.

G.f.: x*(1 + 1013*x + 47840*x^2 + 455192*x^3 + 1310354*x^4 + 1310354*x^5 + 455192*x^6 + 47840*x^7 + 1013*x^8 + x^9)/(1-x)^13. - Vincenzo Librandi, Jan 19 2015

MATHEMATICA

a253710[n_] := Block[{f}, f[1] = 1; f[2] = 1026; f[x_] := 2*f[x - 1] - f[x - 2] + x^10; Array[f, n]]; a253710[21] (* Michael De Vlieger, Jan 11 2015 *)

CoefficientList[Series[(1 + 1013 x + 47840 x^2 + 455192 x^3 + 1310354 x^4 + 1310354 x^5 + 455192 x^6 + 47840 x^7 + 1013 x^8 + x^9) / (1 - x)^13, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 19 2015 *)

CROSSREFS

Sequence in context: A221008 A282254 A229332 * A271761 A229000 A168153

Adjacent sequences:  A253707 A253708 A253709 * A253711 A253712 A253713

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jan 10 2015

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)