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 A356815 #17 Aug 31 2022 09:09:47 %S A356815 1,-2,0,4,32,48,-608,-6400,-24064,163072,3567104,28394496,6535168, %T A356815 -3250745344,-50725740544,-344530853888,2476610551808,110057610608640, %U A356815 1655672654135296,9616664975114240,-195178079811272704,-6998474114188967936,-110894925369151848448 %N A356815 Expansion of e.g.f. exp(-x * (exp(2*x) + 1)). %H A356815 Seiichi Manyama, <a href="/A356815/b356815.txt">Table of n, a(n) for n = 0..499</a> %F A356815 G.f.: Sum_{k>=0} (-x)^k / (1 - (2*k-1)*x)^(k+1). %F A356815 a(n) = Sum_{k=0..n} (-1)^k * (2*k-1)^(n-k) * binomial(n,k). %o A356815 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(exp(2*x)+1)))) %o A356815 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(2*k-1)*x)^(k+1))) %o A356815 (PARI) a(n) = sum(k=0, n, (-1)^k*(2*k-1)^(n-k)*binomial(n, k)); %Y A356815 Cf. A356816, A356818. %Y A356815 Cf. A240165, A351736, A356812. %K A356815 sign %O A356815 0,2 %A A356815 _Seiichi Manyama_, Aug 29 2022