A378090 - OEIS

%I #9 Feb 16 2025 08:34:07

%S 1,4,23,181,1889,25411,427615,8736337,210911489,5882285971,

%T 186121646831,6585885144697,257640988064641,11039620794801691,

%U 514147575711741119,25858553659455655201,1396703647943164718081,80633376290492591578147,4954794080385073122030799

%N E.g.f. satisfies A(x) = exp(x * (1-x)^2 * A(x)) / (1-x)^3.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: exp( -LambertW(-x/(1-x)) )/(1-x)^3.

%F a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2, n-k)/k!);

%Y Cf. A323772, A352410, A378091.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 16 2024