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 A375633 #9 Aug 23 2024 07:29:19
%S A375633 1,1,4,15,84,555,4440,41265,438480,5240025,69582240,1016350335,
%T A375633 16194911040,279560396115,5197054262400,103514720133825,
%U A375633 2199255573715200,49645309340451825,1186599954328588800,29937224154635772975,795051251297099596800
%N A375633 Expansion of e.g.f. exp(x^2) / (1 - x * exp(x^2/2)).
%F A375633 a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+2)/2)^k/k!.
%p A375633 A375633 := proc(n)
%p A375633 n!*add(((n-2*k+2)/2)^k/k!,k=0..floor(n/2)) ;
%p A375633 end proc:
%p A375633 seq(A375633(n),n=0..60) ; # _R. J. Mathar_, Aug 23 2024
%o A375633 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2)/(1-x*exp(x^2/2))))
%o A375633 (PARI) a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/k!);
%Y A375633 Cf. A375394, A375627.
%K A375633 nonn
%O A375633 0,3
%A A375633 _Seiichi Manyama_, Aug 22 2024