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.

A318118 a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).

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%I A318118 #6 Aug 18 2018 11:23:15
%S A318118 1,1,3,10,40,150,616,2456,10102,41400,171526,712111,2972115,12434993,
%T A318118 52195414,219567909,925704792,3909841659,16541598215,70085877919,
%U A318118 297347922785,1263046810334,5370930049915,22861883482838,97402827429118,415332438952517,1772380322197432
%N A318118 a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).
%C A318118 For n > 2, a(n) is the n-th term of the Euler transform of n-gonal numbers.
%H A318118 Vaclav Kotesovec, <a href="/A318118/b318118.txt">Table of n, a(n) for n = 0..1000</a>
%H A318118 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A318118 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F A318118 a(n) ~ c * d^n / sqrt(n), where d = 4.3505530790182509701639869563721679988879373943131559534408716195123... and c = 0.2276354216252041005336767937139336687746108521151301186102034... - _Vaclav Kotesovec_, Aug 18 2018
%t A318118 Table[SeriesCoefficient[Exp[Sum[x^k (1 + (n - 3) x^k)/(k (1 - x^k)^3), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]
%Y A318118 Cf. A000294, A023871, A274998, A278767, A278768, A278769.
%K A318118 nonn
%O A318118 0,3
%A A318118 _Ilya Gutkovskiy_, Aug 18 2018