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 A376515 #12 Feb 16 2025 08:34:07
%S A376515 1,0,2,6,60,480,5880,75600,1197840,20865600,415074240,9067766400,
%T A376515 218808596160,5739600746880,163303845344640,4998933984844800,
%U A376515 164036362839148800,5740920215225395200,213551108122018867200,8412438143909940940800,349915152951011468620800
%N A376515 E.g.f. satisfies A(x) = exp(x^2 * A(x) / (1 - x)).
%H A376515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376515 E.g.f.: exp( -LambertW(-x^2 / (1-x)) ).
%F A376515 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
%F A376515 a(n) ~ exp(1) * sqrt(1 + 4*exp(1) - sqrt(1 + 4*exp(1))) * 2^(n - 1/2) * n^(n-1) / ((1 + 2*exp(1) - sqrt(1 + 4*exp(1))) * (-1 + sqrt(1 + 4*exp(1)))^(n-1)). - _Vaclav Kotesovec_, Sep 26 2024
%o A376515 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2/(1-x)))))
%o A376515 (PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);
%Y A376515 Cf. A052868, A376516.
%Y A376515 Cf. A376494.
%K A376515 nonn,easy
%O A376515 0,3
%A A376515 _Seiichi Manyama_, Sep 26 2024