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 A378090 #17 Aug 05 2025 05:03:46
%S A378090 1,4,23,181,1889,25411,427615,8736337,210911489,5882285971,
%T A378090 186121646831,6585885144697,257640988064641,11039620794801691,
%U A378090 514147575711741119,25858553659455655201,1396703647943164718081,80633376290492591578147,4954794080385073122030799
%N A378090 E.g.f. satisfies A(x) = exp(x * (1-x)^2 * A(x)) / (1-x)^3.
%H A378090 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378090 E.g.f.: exp( -LambertW(-x/(1-x)) )/(1-x)^3.
%F A378090 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2,n-k)/k!.
%F A378090 a(n) ~ n^(n-1) * (1 + exp(1))^(n + 7/2) / exp(n + 5/2). - _Vaclav Kotesovec_, Aug 05 2025
%t A378090 terms = 19; A[_] = 0; Do[A[x_] = Exp[x*(1-x)^2*A[x]]/(1-x)^3 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Mar 24 2025 *)
%o A378090 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2, n-k)/k!);
%Y A378090 Cf. A323772, A352410, A378091.
%K A378090 nonn
%O A378090 0,2
%A A378090 _Seiichi Manyama_, Nov 16 2024