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 A375683 #11 Aug 24 2024 06:04:52
%S A375683 1,0,-2,-3,20,115,-306,-6307,-6616,462663,2956130,-38945951,
%T A375683 -656504388,2325876683,145820995670,562691968005,-33452317341616,
%U A375683 -449954883966065,7055017491780810,233802046526955497,-571834988279277340,-112474674691684827501
%N A375683 Expansion of e.g.f. 1 / (1 + x * (exp(x) - 1)).
%F A375683 a(0) = 1; a(n) = -n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).
%F A375683 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * k! * Stirling2(n-k,k)/(n-k)!.
%o A375683 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*(exp(x)-1))))
%o A375683 (PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*k!*stirling(n-k, k, 2)/(n-k)!);
%Y A375683 Cf. A052848, A367880, A367881.
%Y A375683 Cf. A292893, A375684.
%K A375683 sign
%O A375683 0,3
%A A375683 _Seiichi Manyama_, Aug 24 2024