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 A372315 #13 Feb 16 2025 08:34:06
%S A372315 1,2,8,68,960,18832,471136,14324480,512733696,21119803136,
%T A372315 984029612544,51169331031040,2937675286583296,184560174104465408,
%U A372315 12594824112085327872,927757127285523243008,73369903633161123397632,6200198958236463387836416
%N A372315 Expansion of e.g.f. exp( x - LambertW(-2*x)/2 ).
%H A372315 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372315 a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n,k).
%F A372315 G.f.: Sum_{k>=0} (2*k+1)^(k-1) * x^k / (1-x)^(k+1).
%F A372315 a(n) ~ 2^(n-1) * n^(n-1) * exp((exp(-1) + 1)/2). - _Vaclav Kotesovec_, May 04 2024
%o A372315 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-2*x)/2)))
%o A372315 (PARI) a(n) = sum(k=0, n, (2*k+1)^(k-1)*binomial(n, k));
%Y A372315 Cf. A088957, A360193, A372316, A372320, A372321.
%Y A372315 Cf. A362694.
%K A372315 nonn
%O A372315 0,2
%A A372315 _Seiichi Manyama_, Apr 27 2024