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 A351505 #25 May 12 2022 15:18:42
%S A351505 1,0,0,3,6,20,270,1764,12600,146880,1597680,17934840,243777600,
%T A351505 3506518080,52696595952,870564618000,15354480960000,284780747946240,
%U A351505 5622461683666560,117425971162442880,2574172644658272000,59302473667128599040,1432738540209781728000
%N A351505 Expansion of e.g.f. 1/(1 + x^2/2 * log(1 - x)).
%H A351505 Seiichi Manyama, <a href="/A351505/b351505.txt">Table of n, a(n) for n = 0..443</a>
%F A351505 a(0) = 1; a(n) = n!/2 * Sum_{k=3..n} 1/(k-2) * a(n-k)/(n-k)!.
%F A351505 a(n) = n! * Sum_{k=0..floor(n/3)} k! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
%o A351505 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2/2*log(1-x))))
%o A351505 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!/2*sum(j=3, i, 1/(j-2)*v[i-j+1]/(i-j)!)); v;
%o A351505 (PARI) a(n) = n!*sum(k=0, n\3, k!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y A351505 Cf. A052830, A351506.
%Y A351505 Cf. A351492, A351503,
%K A351505 nonn
%O A351505 0,4
%A A351505 _Seiichi Manyama_, May 04 2022