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.

A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).

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%I A318125 #5 Aug 19 2018 07:27:09
%S A318125 1,1,3,14,54,238,1026,4573,20404,91902,415953,1891908,8638846,
%T A318125 39569655,181766878,836950153,3861927937,17853107055,82668539290,
%U A318125 383360628369,1780126898575,8275908734103,38517137597486,179442212204245,836741558761935,3905012142470483
%N A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).
%C A318125 For n > 2, a(n) is the n-th term of the weigh transform of n-gonal pyramidal numbers.
%H A318125 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A318125 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F A318125 a(n) ~ c * d^n / sqrt(n), where d = 4.761510955746025663058811... and c = 0.2241869836397882024713... - _Vaclav Kotesovec_, Aug 19 2018
%t A318125 Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k (1 + (n - 3) x^k)/(k (1 - x^k)^4), {k, 1, n}]], {x, 0, n}], {n, 0, 25}]
%Y A318125 Cf. A258343, A281156, A294842, A294843, A294844, A294845, A318121, A318124.
%K A318125 nonn
%O A318125 0,3
%A A318125 _Ilya Gutkovskiy_, Aug 18 2018