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 A380339 #10 Jan 22 2025 06:39:27
%S A380339 0,0,0,3,6,20,0,-126,-1260,3240,108360,1635480,15075720,119957760,
%T A380339 705729024,6324040800,130989549600,3572031415680,78736127656320,
%U A380339 1502102645890560,25514633892182400,423898384988494080,7590291773745542400,162254912688831916800,4023271392778314673920
%N A380339 Expansion of e.g.f. log(1 - x^2/2 * log(1 - x)).
%F A380339 a(n) = n! * Sum_{k=1..floor(n/3)} (-1)^(k-1) * (k-1)! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
%F A380339 a(0) = a(1) = a(2) = 0; a(n) = n!/(2*(n-2)) - Sum_{k=3..n-1} k!/(2*(k-2)) * binomial(n-1,k) * a(n-k).
%o A380339 (PARI) a(n) = n!*sum(k=1, n\3, (-1)^(k-1)*(k-1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y A380339 Cf. A089064, A380338.
%Y A380339 Cf. A368165, A368173.
%K A380339 sign
%O A380339 0,4
%A A380339 _Seiichi Manyama_, Jan 22 2025