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 A355508 #40 Sep 12 2022 03:05:03
%S A355508 1,0,0,6,12,20,1830,15162,82376,3326472,59467050,678585710,
%T A355508 20553790092,563969783676,10776243950654,318310813941330,
%U A355508 10988438698692240,303144002003606672,9910024990673571666,392381835437286982998,14072003919511407720020
%N A355508 E.g.f. satisfies log(A(x)) = x^2 * (exp(x * A(x)) - 1) * A(x).
%F A355508 a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.
%t A355508 m = 21; (* number of terms *)
%t A355508 A[_] = 0;
%t A355508 Do[A[x_] = Exp[x^2*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
%t A355508 CoefficientList[A[x], x]*Range[0, m - 1]! (* _Jean-François Alcover_, Sep 12 2022 *)
%o A355508 (PARI) a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);
%Y A355508 Cf. A349557, A356785, A356892.
%Y A355508 Cf. A356962.
%K A355508 nonn
%O A355508 0,4
%A A355508 _Seiichi Manyama_, Sep 07 2022