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 A356632 #13 Nov 01 2022 11:24:55
%S A356632 1,1,2,9,48,330,2880,29610,362880,5148360,83462400,1535549400,
%T A356632 31614105600,724183059600,18307441152000,507367438578000,
%U A356632 15336404987904000,502812808754256000,17805001275629568000,678167395781763888000,27681559049033809920000
%N A356632 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/2^k.
%F A356632 E.g.f.: Sum_{k>=0} x^k / (1 - k*x^2/2).
%F A356632 a(n) ~ Pi * exp((1/LambertW(exp(1)*n/2) - 3)*n/2) * n^(3*n/2 + 1) / (sqrt(1 + LambertW(exp(1)*n/2)) * 2^((n-1)/2) * LambertW(exp(1)*n/2)^((n+1)/2)). - _Vaclav Kotesovec_, Nov 01 2022
%t A356632 a[n_] := n! * Sum[(n - 2*k)^k/2^k, {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 21, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356632 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/2^k);
%o A356632 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^2/2))))
%Y A356632 Cf. A356633, A356634.
%Y A356632 Cf. A352944.
%K A356632 nonn
%O A356632 0,3
%A A356632 _Seiichi Manyama_, Aug 18 2022