A378017 - OEIS

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

%S 1,3,15,148,2077,38326,883369,24431436,789531705,29213730010,

%T 1218401262541,56566561281616,2893886178904549,161768999193007974,

%U 9811122121462081281,641683497800057913556,45022670799746182036465,3373421864644139722767538,268843153008388446079159573

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

%F a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+2,n-k)/k!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^2*exp(-lambertw(-x*(1+x)^3))))

%o (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+2, n-k)/k!);

%Y Cf. A376145, A377828, A378016.

%Y Cf. A377966.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 14 2024