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 A372158 #16 Aug 05 2025 06:43:25
%S A372158 1,2,12,110,1368,21602,415036,9416094,246730448,7340456258,
%T A372158 244615296564,9030708939518,365998814372824,16159576541122146,
%U A372158 772216069907880812,39715949460883093598,2187682975276318552224,128508919233259720967810
%N A372158 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) / (1 - x) ).
%H A372158 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372158 E.g.f.: A(x) = exp( -2 * LambertW(-x / (1-x)) ).
%F A372158 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(n+(s-1)*k-1,n-k)/k!.
%F A372158 a(n) ~ 2 * exp(2) * (1 + exp(-1))^(n + 1/2) * n^(n-1). - _Vaclav Kotesovec_, Aug 05 2025
%o A372158 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*lambertw(-x/(1-x)))))
%o A372158 (PARI) a(n, r=2, s=1, t=1, u=0) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
%Y A372158 Cf. A052868, A372159.
%K A372158 nonn
%O A372158 0,2
%A A372158 _Seiichi Manyama_, Apr 20 2024