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 A377595 #74 Aug 05 2025 07:25:10
%S A377595 1,2,11,103,1377,24101,523813,13636463,414246017,14396807161,
%T A377595 563682761541,24559156435595,1178780540094193,61810491468265541,
%U A377595 3515914378433242997,215647516162031069191,14187967957218808201089,996767406049512569338481,74478502236949781909301253
%N A377595 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x).
%H A377595 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377595 E.g.f.: exp( -LambertW(-x/(1-x)^2) )/(1-x).
%F A377595 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+k,n-k)/k!.
%F A377595 a(n) ~ sqrt(1 + 2*exp(-1) - sqrt(1 + 4*exp(-1))) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * 2^(n + 3/2) * n^(n-1) / ((sqrt(1 + 4*exp(-1)) - 1)^(5/2) * exp(n) * (2 + exp(1) - exp(1/2)*sqrt(4 + exp(1)))^n). - _Vaclav Kotesovec_, Aug 05 2025
%o A377595 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))/(1-x)))
%o A377595 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+k, n-k)/k!);
%Y A377595 Cf. A362775, A377810.
%Y A377595 Cf. A361598.
%K A377595 nonn
%O A377595 0,2
%A A377595 _Seiichi Manyama_, Nov 14 2024