cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A047682 a(n) = 4^(2*n)*(4^(2*n)-1)*Bernoulli(2*n)/(2*n).

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%I A047682 #21 Mar 28 2024 23:54:45
%S A047682 20,-544,66560,-17895424,8329625600,-5937093935104,6004799480791040,
%T A047682 -8176700159200067584,14421891569272362106880,
%U A047682 -31983597922505761818148864,87107695717210805652024197120,-285816431841945942589104606674944,1112035502745012017553352712530165760
%N A047682 a(n) = 4^(2*n)*(4^(2*n)-1)*Bernoulli(2*n)/(2*n).
%D A047682 J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton, 1974, p. 283.
%H A047682 Andrew Howroyd, <a href="/A047682/b047682.txt">Table of n, a(n) for n = 1..100</a>
%H A047682 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.
%t A047682 f[n_]:=Module[{c=2n,x},x=4^c;(x(x-1)BernoulliB[c])/c]; Array[f,20] (* _Harvey P. Dale_, Feb 19 2013 *)
%o A047682 (PARI) a(n) = 4^(2*n)*(4^(2*n)-1)*bernfrac(2*n)/(2*n) \\ _Andrew Howroyd_, May 18 2020
%Y A047682 Column 3 of A241066.
%Y A047682 Row sums of even-indexed rows of A211233.
%K A047682 sign
%O A047682 1,1
%A A047682 _N. J. A. Sloane_
%E A047682 Offset corrected and terms a(13) and beyond from _Andrew Howroyd_, May 18 2020