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 A376577 #15 Feb 16 2025 08:34:07
%S A376577 1,1,3,22,197,2256,32887,574624,11690121,272279296,7147894571,
%T A376577 208828168704,6721780173517,236392313927680,9019055052313503,
%U A376577 371059593102831616,16376333449953390353,771800236449984086016,38687542995415388643667,2055303661966287413837824
%N A376577 E.g.f. A(x) satisfies A(x) = exp(x*(1 + x^2)*A(x)).
%H A376577 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376577 a(n) = n! * Sum_{k=0..floor(n/3)} (n-2*k+1)^(n-2*k-1) * binomial(n-2*k,k)/(n-2*k)!.
%F A376577 E.g.f.: exp( -LambertW(-x*(1+x^2)) ).
%F A376577 a(n) ~ sqrt(3 - 2*r*exp(1)) * n^(n-1) / (exp(n-1) * r^n), where r = 0.3314625163779096554724... is the real root of the equation r*(1 + r^2) = exp(-1). - _Vaclav Kotesovec_, Sep 29 2024
%o A376577 (PARI) a(n) = n!*sum(k=0, n\3, (n-2*k+1)^(n-2*k-1)*binomial(n-2*k, k)/(n-2*k)!);
%o A376577 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(1+x^2)))))
%Y A376577 Cf. A362771, A376578.
%K A376577 nonn
%O A376577 0,3
%A A376577 _Seiichi Manyama_, Sep 28 2024