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 A378047 #15 Feb 16 2025 08:34:07
%S A378047 1,3,11,70,685,8966,147769,2938608,68509193,1832813866,55354862701,
%T A378047 1863179311676,69163696768093,2807246931378462,123685264726805825,
%U A378047 5879149578658117096,299892675674572370065,16340561709320173229906,947234845622653951286485
%N A378047 E.g.f. satisfies A(x) = (1+x)^2 * exp(x * A(x) / (1+x)).
%H A378047 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378047 E.g.f.: (1+x)^2 * exp( -LambertW(-x*(1+x)) ).
%F A378047 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(k+2,n-k)/k!.
%F A378047 a(n) ~ (1 + sqrt(1 + 4*exp(-1)))^2 * sqrt(2 + 8*exp(-1) - 2*sqrt(1 + 4*exp(-1))) * 2^(n-3) * n^(n-1) / ((sqrt(1 + 4*exp(-1)) - 1)^n * exp(n - 3/2)). - _Vaclav Kotesovec_, Nov 15 2024
%o A378047 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(k+2, n-k)/k!);
%Y A378047 Cf. A362771, A377826.
%K A378047 nonn
%O A378047 0,2
%A A378047 _Seiichi Manyama_, Nov 15 2024