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.

A375665 Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^3.

This page as a plain text file.
%I A375665 #10 Sep 01 2024 09:35:06
%S A375665 1,0,0,18,0,180,4320,2520,241920,3674160,12700800,599749920,
%T A375665 7903526400,77863705920,2660390853120,37269497865600,683129089843200,
%U A375665 19948163057222400,339567800885913600,8690022866119795200,241333983478748160000,5217670959100125926400
%N A375665 Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^3.
%F A375665 E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375588.
%F A375665 a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * Stirling2(k,n-2*k)/k!.
%o A375665 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^3))
%o A375665 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/2;
%Y A375665 Cf. A375588, A375664.
%K A375665 nonn
%O A375665 0,4
%A A375665 _Seiichi Manyama_, Aug 23 2024