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 A378091 #17 Aug 05 2025 05:06:02
%S A378091 1,5,33,280,3009,40456,670351,13428794,318341841,8747362540,
%T A378091 273595272231,9595433139238,372786185735497,15885841209363152,
%U A378091 736549352642825247,36906793949098033906,1987212351128733260577,114415986259681057007956,7014281833059332148174007
%N A378091 E.g.f. satisfies A(x) = exp(x * (1-x)^3 * A(x)) / (1-x)^4.
%H A378091 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378091 E.g.f.: exp( -LambertW(-x/(1-x)) )/(1-x)^4.
%F A378091 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+3,n-k)/k!.
%F A378091 a(n) ~ n^(n-1) * (1 + exp(1))^(n + 9/2) / exp(n + 7/2). - _Vaclav Kotesovec_, Aug 05 2025
%t A378091 terms = 19; A[_] = 0; Do[A[x_] = Exp[x*(1-x)^3*A[x]]/(1-x)^4 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Mar 24 2025 *)
%o A378091 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+3, n-k)/k!);
%Y A378091 Cf. A323772, A352410, A378090.
%K A378091 nonn
%O A378091 0,2
%A A378091 _Seiichi Manyama_, Nov 16 2024