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 A372157 #16 Feb 16 2025 08:34:06
%S A372157 1,3,15,99,837,8583,104229,1463031,23362089,418489227,8318989089,
%T A372157 181823016147,4335947796717,112073459278095,3122026815194205,
%U A372157 93267116190237807,2974988801559127761,100932108044810678547,3629658464478098931897,137928467585817206673291
%N A372157 E.g.f. A(x) satisfies A(x) = exp( 3 * x * (1 + x * A(x)^(1/3)) ).
%H A372157 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372157 E.g.f.: A(x) = exp( 3*x - 3*LambertW(-x^2 * exp(x)) ).
%F A372157 If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(s*k,n-k)/k!.
%o A372157 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*x-3*lambertw(-x^2*exp(x)))))
%o A372157 (PARI) a(n, r=3, s=1, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);
%Y A372157 Cf. A125500, A372156.
%K A372157 nonn
%O A372157 0,2
%A A372157 _Seiichi Manyama_, Apr 20 2024