A378092 - OEIS

%I #10 Feb 16 2025 08:34:07

%S 1,2,11,118,1993,46386,1376059,49601014,2104366513,102717184546,

%T 5670357524011,349304240222070,23754501885783673,1767641331001915474,

%U 142868173684094891803,12463599550013379095926,1167281368458948415748833,116814664082977998388994370,12440156205235958837516345419

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

%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(-2*x/(1-x))/2 )/(1-x).

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

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

%Y Cf. A352410, A378093.

%Y Cf. A378041.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 16 2024