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 A189423 #31 Feb 19 2025 10:25:29
%S A189423 1,1,2,0,10,-50,368,-3052,28740,-302220,3508152,-44532048,613399752,
%T A189423 -9109006920,145029146208,-2463935369040,44482964644368,
%U A189423 -850291412311152,17153458120885152,-364163960169826944,8114899768747511712,-189364681355153357088,4617713773733245962240
%N A189423 Expansion of e.g.f. exp(log(1+x) + log(1+x)^2).
%H A189423 Seiichi Manyama, <a href="/A189423/b189423.txt">Table of n, a(n) for n = 0..447</a>
%H A189423 Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F A189423 a(0) = 1; a(n) = Sum_{m=1..n} Sum_{k=m..n} k!*binomial(m,k-m)*stirling1(n,k)/m! for n>0.
%F A189423 a(n) = Sum_{k=0..n} A047974(k) * Stirling1(n,k). - _Seiichi Manyama_, May 14 2022
%o A189423 (Maxima)
%o A189423 a(n):=sum(sum(k!*binomial(m,k-m)*stirling1(n,k),k,m,n)/m!,m,1,n);
%o A189423 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)*(1+log(1+x))))) \\ _Seiichi Manyama_, May 14 2022
%o A189423 (PARI) a(n) = sum(k=0, n, k!*sum(j=0, k\2, 1/(j!*(k-2*j)!))*stirling(n, k, 1)); \\ _Seiichi Manyama_, May 14 2022
%Y A189423 Cf. A005444, A047974.
%K A189423 sign
%O A189423 0,3
%A A189423 _Vladimir Kruchinin_, Apr 21 2011