cp's OEIS Frontend

A253711 Second partial sums of 11th powers (A008455).

%I A253711 #47 Jun 13 2015 00:55:21
%S A253711 1,2050,181246,4554746,57756371,473755052,2867080476,13850340492,
%T A253711 56214660117,198578979742,626254969978,1796939330902,4759784085863,
%U A253711 11772194010488,27434359794488,60688711622904,128214959758953,260009617974234,508294535087734,961379452201234,1764741869856955,3152422588924004,5492913065904980
%N A253711 Second partial sums of 11th powers (A008455).
%C A253711 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.
%H A253711 Luciano Ancora, <a href="/A253636/a253636_3.pdf">Recurrence relation for the second partial sums of m-th powers</a>
%H A253711 Luciano Ancora, <a href="/A253636/a253636_4.pdf">Second partial sums of the m-th powers</a>
%H A253711 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A253711 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.
%F A253711 a(n) = 2*a(n-1) - a(n-2) + n^11.
%F A253711 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
%t A253711 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 *)
%t A253711 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 *)
%Y A253711 Cf. A008455.
%K A253711 nonn,easy
%O A253711 1,2
%A A253711 _Luciano Ancora_, Jan 10 2015