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 A371040 #12 Feb 16 2025 08:34:06
%S A371040 1,1,2,12,96,840,9720,143640,2399040,45239040,976752000,23537606400,
%T A371040 621444700800,17936155036800,562855739846400,19038932398886400,
%U A371040 690456599575142400,26748823900403404800,1102407824344284057600,48147134965603914240000
%N A371040 E.g.f. satisfies A(x) = exp(x^3*A(x)^2) / (1-x).
%H A371040 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A371040 E.g.f.: sqrt(LambertW( -2*x^3/(1-x)^2 ) / (-2*x^3)).
%F A371040 a(n) = n! * Sum_{k=0..floor(n/3)} (2*k+1)^(k-1) * binomial(n-k,n-3*k)/k!.
%o A371040 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x^3/(1-x)^2)/(-2*x^3))))
%o A371040 (PARI) a(n) = n!*sum(k=0, n\3, (2*k+1)^(k-1)*binomial(n-k, n-3*k)/k!);
%Y A371040 Cf. A360601, A370875.
%K A371040 nonn
%O A371040 0,3
%A A371040 _Seiichi Manyama_, Mar 09 2024