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 A372320 #12 Feb 16 2025 08:34:06
%S A372320 -1,0,4,36,464,8560,206112,6104896,214376192,8701657344,400748710400,
%T A372320 20642974511104,1175888936749056,73389707156586496,
%U A372320 4980134850525986816,365062349226075463680,28747688571714736160768,2420266280392895064506368
%N A372320 Expansion of e.g.f. -exp( x + LambertW(-2*x)/2 ).
%H A372320 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372320 a(n) = Sum_{k=0..n} (2*k-1)^(k-1) * binomial(n,k).
%F A372320 G.f.: Sum_{k>=0} (2*k-1)^(k-1) * x^k / (1-x)^(k+1).
%F A372320 a(n) ~ 2^(n-1) * n^(n-1) * exp((exp(-1) - 1)/2). - _Vaclav Kotesovec_, May 06 2024
%o A372320 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x+lambertw(-2*x)/2)))
%o A372320 (PARI) a(n) = sum(k=0, n, (2*k-1)^(k-1)*binomial(n, k));
%Y A372320 Cf. A088957, A360193, A372315, A372316, A372321.
%K A372320 sign
%O A372320 0,3
%A A372320 _Seiichi Manyama_, Apr 27 2024