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 A371041 #11 Feb 16 2025 08:34:06
%S A371041 1,1,4,30,348,5460,108480,2609040,73713360,2393087760,87791891040,
%T A371041 3591843726240,162157925160000,8007919490450880,429418816003457280,
%U A371041 24849579630222547200,1543505958412498080000,102430107277414595078400,7232759636684706937612800
%N A371041 E.g.f. satisfies A(x) = exp(x^2*A(x)^3) / (1-x).
%H A371041 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A371041 E.g.f.: (LambertW( -3*x^2/(1-x)^3 ) / (-3*x^2))^(1/3).
%F A371041 a(n) = n! * Sum_{k=0..floor(n/2)} (3*k+1)^(k-1) * binomial(n+k,n-2*k)/k!.
%o A371041 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x^2/(1-x)^3)/(-3*x^2))^(1/3)))
%o A371041 (PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*binomial(n+k, n-2*k)/k!);
%Y A371041 Cf. A360609, A370876.
%K A371041 nonn
%O A371041 0,3
%A A371041 _Seiichi Manyama_, Mar 09 2024