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 A377608 #38 Feb 16 2025 08:34:07
%S A377608 1,3,19,202,3085,61886,1544029,46182900,1612759369,64455582394,
%T A377608 2902794546961,145497909334856,8035136800888333,484821204654219798,
%U A377608 31735810390729211173,2240132583683741633116,169624462686462529305745,13715713402047448280358002,1179576532854283015832748697
%N A377608 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x)^2.
%H A377608 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377608 E.g.f.: exp( -LambertW(-x/(1-x)^3) )/(1-x)^2.
%F A377608 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2*k+1,n-k)/k!.
%o A377608 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^2))
%o A377608 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k+1, n-k)/k!);
%Y A377608 Cf. A367789, A377599, A377811.
%K A377608 nonn
%O A377608 0,2
%A A377608 _Seiichi Manyama_, Nov 14 2024