cp's OEIS Frontend

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.

A356818 Expansion of e.g.f. exp(-x * (exp(x) + 1)).

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%I A356818 #12 Aug 31 2022 09:09:42
%S A356818 1,-2,2,1,0,-17,-32,103,976,2287,-12816,-143585,-481016,2339335,
%T A356818 39769720,209863327,-397553376,-16949434913,-142681662368,
%U A356818 -233212601153,9138353475736,128343346833463,702261255539496,-4251314594919617,-135331386127555856
%N A356818 Expansion of e.g.f. exp(-x * (exp(x) + 1)).
%H A356818 Seiichi Manyama, <a href="/A356818/b356818.txt">Table of n, a(n) for n = 0..558</a>
%F A356818 G.f.: Sum_{k>=0} (-x)^k / (1 - (k-1)*x)^(k+1).
%F A356818 a(n) = Sum_{k=0..n} (-1)^k * (k-1)^(n-k) * binomial(n,k).
%o A356818 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(x)+1))))
%o A356818 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(k-1)*x)^(k+1)))
%o A356818 (PARI) a(n) = sum(k=0, n, (-1)^k*(k-1)^(n-k)*binomial(n, k));
%Y A356818 Cf. A356815, A356816.
%K A356818 sign
%O A356818 0,2
%A A356818 _Seiichi Manyama_, Aug 29 2022