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 A356628 #20 Nov 01 2022 11:55:53
%S A356628 1,1,1,7,25,181,1561,12811,188497,2071945,38889361,620762671,
%T A356628 12917838121,291278938237,6667342764265,194869722610291,
%U A356628 5137978752994081,177509783765281681,5610285632192738977,215195998789004395735,8228064506323330305721
%N A356628 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(n - 2*k)!.
%H A356628 Seiichi Manyama, <a href="/A356628/b356628.txt">Table of n, a(n) for n = 0..366</a>
%F A356628 E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^2)).
%F A356628 a(n) ~ sqrt(Pi) * exp((n-1)/(2*LambertW(exp(1/3)*(n-1)/3)) - 3*n/2) * n^((3*n + 1)/2) / (sqrt(1 + LambertW(exp(1/3)*(n - 1)/3)) * 3^((n+1)/2) * LambertW(exp(1/3)*(n-1)/3)^(n/2)). - _Vaclav Kotesovec_, Nov 01 2022
%t A356628 a[n_] := n! * Sum[(n - 2*k)^k/(n - 2*k)!, {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 21, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356628 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(n-2*k)!);
%o A356628 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^2)))))
%Y A356628 Cf. A354436, A356629, A356630.
%Y A356628 Cf. A216688, A356632, A358064.
%K A356628 nonn
%O A356628 0,4
%A A356628 _Seiichi Manyama_, Aug 18 2022