The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A123094 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A123094

Sum of first n 12th powers.
(history; published version)

#46 by Michael De Vlieger at Mon May 27 12:58:22 EDT 2024

STATUS

proposed

approved

#45 by Michel Marcus at Mon May 27 12:13:24 EDT 2024

STATUS

editing

proposed

#44 by Michel Marcus at Mon May 27 00:01:14 EDT 2024

LINKS

B. Bruno Berselli, A description of the recursive method in Formula lines (first formula): website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).

FORMULA

a(n) = (-1)*Sum_{j=1..12} j*sStirling1(n+1,n+1-j)*SStirling2(n+12-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

STATUS

approved

editing

#43 by Charles R Greathouse IV at Thu Sep 08 08:45:28 EDT 2022

PROG

(MAGMAMagma) [(&+[j^12: j in [0..n]]): j in [0..30]]; // G. C. Greubel, Jul 21 2021

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#42 by Sean A. Irvine at Sat Aug 14 21:41:06 EDT 2021

STATUS

proposed

approved

#41 by Michel Marcus at Thu Jul 22 01:00:53 EDT 2021

STATUS

editing

proposed

#40 by Michel Marcus at Thu Jul 22 01:00:33 EDT 2021

CROSSREFS

Cf. A008275, A008277.

#39 by Michel Marcus at Thu Jul 22 00:59:20 EDT 2021

CROSSREFS

Cf. A008456, A215083.

STATUS

proposed

editing

#38 by G. C. Greubel at Wed Jul 21 16:56:01 EDT 2021

STATUS

editing

proposed

#37 by G. C. Greubel at Wed Jul 21 16:55:55 EDT 2021

FORMULA

a(n) = n*A123095(n) - sum(Sum_{i=0..n-1, } A123095(i)). - Bruno Berselli, Apr 27 2010

a(n) =-sum (-1)*Sum_{j=1..12, } j*s(n+1,n+1-j)*S(n+12-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

MATHEMATICA

lst={}; s=0; Do[s=s+n^12; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^12, {k, 1, n}], {n, 0, 10030}] (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)

PROG

(Sage) [bernoulli_polynomial(n, 13)/13 for n in range(1, 1930)] # Zerinvary Lajos, May 17 2009

(MAGMA) [(&+[j^12: j in [0..n]]): j in [0..30]]; // G. C. Greubel, Jul 21 2021

CROSSREFS

Sequences of the form Sum_{j=0..n} j^m : A000217 (m=1), A000330 (m=2), A000537 (m=3), A000538 (m=4), A000539 (m=5), A000540 (m=6), A000541 (m=7), A000542 (m=8), A007487 (m=9), A023002 (m=10), A123095 (m=11), this sequence (m=12), A181134 (m=13).

Cf. A215083.

STATUS

approved

editing