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 A361594 #13 Oct 29 2023 12:55:09
%S A361594 1,1,4,24,180,1620,17040,204960,2770320,41504400,681791040,
%T A361594 12173293440,234555773760,4847900016960,106932303878400,
%U A361594 2506094618227200,62165827044921600,1626693694039814400,44767280999939097600,1292282276155782912000
%N A361594 Expansion of e.g.f. exp( (x / (1-x))^2 ) / (1-x).
%F A361594 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n,2*k)/k!.
%F A361594 From _Vaclav Kotesovec_, Mar 17 2023: (Start)
%F A361594 a(n) = (3*n - 2)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-2)^2*(n-1)*a(n-3).
%F A361594 a(n) ~ 2^(-1/6) * 3^(-1/2) * exp(1/3 - 2^(-1/3)*n^(1/3) + 3*2^(-2/3)*n^(2/3) - n) * n^(n + 1/6) * (1 + 11*2^(1/3)/(27*n^(1/3)) - 79/(3645*2^(1/3)*n^(2/3))). (End)
%t A361594 Table[n! * Sum[Binomial[n,2*k]/k!, {k,0,n/2}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%t A361594 With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^2]/(1-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 29 2023 *)
%o A361594 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^2)/(1-x)))
%Y A361594 Cf. A002720, A361595.
%Y A361594 Cf. A052887.
%K A361594 nonn
%O A361594 0,3
%A A361594 _Seiichi Manyama_, Mar 16 2023