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 A361596 #11 Mar 17 2023 08:27:58
%S A361596 1,1,3,15,99,795,7485,80745,981225,13253625,196834995,3185662095,
%T A361596 55770765435,1049572599075,21120725230605,452384160453225,
%U A361596 10272547048388625,246434674107647025,6226347228582355875,165224032352989584975,4593512876411509125075
%N A361596 Expansion of e.g.f. exp( x^2/(2 * (1-x)^2) ) / (1-x).
%F A361596 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n,2*k)/(2^k * k!).
%F A361596 From _Vaclav Kotesovec_, Mar 17 2023: (Start)
%F A361596 a(n) = (3*n - 2)*a(n-1) - (n-1)*(3*n - 5)*a(n-2) + (n-2)^2*(n-1)*a(n-3).
%F A361596 a(n) ~ 3^(-1/2) * exp(1/6 - n^(1/3)/2 + 3*n^(2/3)/2 - n) * n^(n + 1/6) * (1 + 49/(108*n^(1/3)) + 3293/(116640*n^(2/3))). (End)
%t A361596 Table[n! * Sum[Binomial[n,2*k]/(2^k * k!), {k,0,n/2}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%o A361596 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(2*(1-x)^2))/(1-x)))
%Y A361596 Cf. A002720, A361597.
%Y A361596 Cf. A335344.
%K A361596 nonn
%O A361596 0,3
%A A361596 _Seiichi Manyama_, Mar 16 2023