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 A377810 #9 Feb 16 2025 08:34:07
%S A377810 1,3,17,154,1993,34066,728209,18733926,564117425,19473863986,
%T A377810 758421401401,32901791851006,1573602042306265,82267318018246986,
%U A377810 4667656830688700801,285662368622361581206,18758565855176593500385,1315663025587514658845026,98160436697525045768511721
%N A377810 E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^2.
%H A377810 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377810 E.g.f.: exp( -LambertW(-x/(1-x)^2) )/(1-x)^2.
%F A377810 E.g.f.: -LambertW(-x/(1-x)^2)/x.
%F A377810 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+k+1,n-k)/k!.
%F A377810 a(n) ~ 2^(n + 3/2) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(3/2) * (1 + 2*exp(-1) - sqrt(1 + 4*exp(-1)))^(n + 1/2) * exp(2*n+1)). - _Vaclav Kotesovec_, Nov 11 2024
%o A377810 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))/(1-x)^2))
%o A377810 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+k+1, n-k)/k!);
%Y A377810 Cf. A352410, A377811.
%Y A377810 Cf. A362775, A377742.
%K A377810 nonn
%O A377810 0,2
%A A377810 _Seiichi Manyama_, Nov 08 2024