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A123095 Sum of first n 11th powers. 3
0, 1, 2049, 179196, 4373500, 53201625, 415998681, 2393325424, 10983260016, 42364319625, 142364319625, 427675990236, 1170684360924, 2962844754961, 7012409924625, 15662165784000, 33254351828416, 67526248136049 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence is related to A023002 by a(n) = n*A023002(n) - sum(A023002(i), i=0..n-1). - Bruno Berselli, Apr 27 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

FORMULA

a(n) = n^2*(n+1)^2*(2*n^8+8*n^7+4*n^6-16*n^5-5*n^4+26*n^3-3*n^2-20*n+10)/24. - Bruno Berselli, Oct 03 2010

G.f.: x*(x^10 +2036*x^9 +152637*x^8 +2203488*x^7 +9738114*x^6 +15724248*x^5 +9738114*x^4 +2203488*x^3 +152637*x^2 +2036*x +1)/(1-x)^13. - Colin Barker, May 27 2012

a(n)=-sum(j=1..11, j*s(n+1,n+1-j)*S(n+11-j,n)), where s(n,k) and S(n,k) are the Stirling numbers of the first kind and the second kind, respectively. - Mircea Merca, Jan 25 2014

MAPLE

[seq(add(i^11, i=1..n), n=0..20)];

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^11 od: seq(a[n], n=0..13); # Zerinvary Lajos, Feb 22 2008

MATHEMATICA

lst={}; s=0; Do[s=s+n^11; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^11, {k, 1, n}], {n, 0, 10^2}] (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)

PROG

(Python)

A123095_list, m = [0], [39916800, -199584000, 419126400, -479001600, 322494480, -129230640, 29607600, -3498000, 171006, -2046, 1, 0 , 0]

for _ in range(10**2):

....for i in range(12):

........m[i+1]+= m[i]

....A123095_list.append(m[-1]) # Chai Wah Wu, Nov 05 2014

CROSSREFS

Cf. A023002.

Sequence in context: A017685 A013959 A036089 * A174752 A045059 A224119

Adjacent sequences:  A123092 A123093 A123094 * A123096 A123097 A123098

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos, Sep 27 2006

STATUS

approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)