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 A376517 #13 Feb 16 2025 08:34:07
%S A376517 1,0,2,6,36,360,3000,40320,532560,8527680,152591040,2987107200,
%T A376517 65408333760,1544664401280,39767121313920,1100734899264000,
%U A376517 32661264290054400,1034874195222067200,34834463447361177600,1242657968679512985600,46804841790705090892800
%N A376517 E.g.f. satisfies A(x) = exp(x^2 * (1 + x) * A(x)).
%H A376517 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376517 E.g.f.: exp( -LambertW(-x^2 * (1+x)) ).
%F A376517 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(k,n-2*k)/k!.
%F A376517 a(n) ~ sqrt((2 + 3*r)/(1 + r)) * n^(n-1) / (exp(n-1) * r^n), where r = (-1 + 2*cosh(log(-1 + (3*(9 + sqrt(81 - 12*exp(1))))/(2*exp(1)))/3))/3. - _Vaclav Kotesovec_, Sep 26 2024
%o A376517 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2*(1+x)))))
%o A376517 (PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(k, n-2*k)/k!);
%Y A376517 Cf. A362771, A376518.
%Y A376517 Cf. A376492, A376512.
%K A376517 nonn,easy
%O A376517 0,3
%A A376517 _Seiichi Manyama_, Sep 26 2024