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.
%I A358264 #10 Nov 13 2022 04:41:27 %S A358264 1,1,2,9,48,315,2520,23415,248640,2972025,39463200,576413145, %T A358264 9184855680,158550787395,2947473809280,58707685211175, %U A358264 1247293022976000,28156003910859825,672972205556851200,16978695795089253225,450907982644863744000,12573634144960773960075 %N A358264 Expansion of e.g.f. 1/(1 - x * exp(x^2/2)). %F A358264 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k!). %F A358264 a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n/2)). - _Vaclav Kotesovec_, Nov 13 2022 %o A358264 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2/2)))) %o A358264 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!)); %Y A358264 Cf. A006153, A358265. %Y A358264 Cf. A354550, A358064. %K A358264 nonn,easy %O A358264 0,3 %A A358264 _Seiichi Manyama_, Nov 06 2022