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 A380338 #16 Jan 22 2025 06:39:38
%S A380338 0,0,2,3,-4,-30,54,1260,3856,-36288,-279000,2970000,56725008,
%T A380338 109343520,-5495740992,-26086263840,1293641890560,21771049466880,
%U A380338 -45508965806592,-4589738336217600,10493846174810880,2423866077943511040,34328754265480012800,-358930542362135546880
%N A380338 Expansion of e.g.f. log(1 - x * log(1 - x)).
%F A380338 a(n) = n! * Sum_{k=1..floor(n/2)} (-1)^(k-1) * (k-1)! * |Stirling1(n-k,k)|/(n-k)!.
%F A380338 a(0) = a(1) = 0; a(n) = n * (n-2)! - Sum_{k=2..n-1} k * (k-2)! * binomial(n-1,k) * a(n-k).
%o A380338 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(log(1-x*log(1-x)))))
%o A380338 (PARI) a(n) = n!*sum(k=1, n\2, (-1)^(k-1)*(k-1)!*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A380338 Cf. A052804, A052858.
%Y A380338 Cf. A089064, A380339.
%Y A380338 Cf. A001048, A375684.
%K A380338 sign
%O A380338 0,3
%A A380338 _Seiichi Manyama_, Jan 21 2025