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A253711 Second partial sums of 11th powers (A008455). 0
1, 2050, 181246, 4554746, 57756371, 473755052, 2867080476, 13850340492, 56214660117, 198578979742, 626254969978, 1796939330902, 4759784085863, 11772194010488, 27434359794488, 60688711622904, 128214959758953, 260009617974234, 508294535087734, 961379452201234, 1764741869856955, 3152422588924004, 5492913065904980 (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..23.

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

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

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

FORMULA

a(n) = n*(n+1)*(n+2)*(70*n^10 + 700*n^9 + 2310*n^8 + 1680*n^7 - 4655*n^6 - 4410*n^5 + 8240*n^4 + 4120*n^3 - 7819*n^2 + 202*n + 1382)/10920.

a(n) = 2*a(n-1) - a(n-2) + n^11.

G.f.: x*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10) / (1 - x)^14. - Vincenzo Librandi, Jan 15 2015

MATHEMATICA

Table[n (n + 1) (n + 2) (70 n^10 + 700 n^9 + 2310 n^8 + 1680 n^7 - 4655 n^6 - 4410 n^5 + 8240 n^4 + 4120 n^3 - 7819 n^2 + 202 n + 1382)/10920, {n, 1, 20}] (* Vincenzo Librandi, Jan 15 2015 *)

RecurrenceTable[{a[n] == 2 a[n - 1] - a[n - 2] + n^11, a[1] == 1, a[2] == 2050}, a, {n, 1, 20}] (* Bruno Berselli, Jan 15 2015 *)

CROSSREFS

Cf. A008455.

Sequence in context: A045059 A224119 A183842 * A168176 A224728 A224721

Adjacent sequences:  A253708 A253709 A253710 * A253712 A253713 A253714

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jan 10 2015

STATUS

approved

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