A367789 E.g.f. satisfies A(x) = exp( x/(1-x)^3 * A(x) ).

1, 1, 9, 106, 1697, 35076, 893947, 27165706, 960298593, 38751082552, 1758831242291, 88726543365054, 4926355857050641, 298605321687360676, 19623211558172733435, 1389870724939251455506, 105556814502357807727553, 8557797733469700008170224

Offset: 0

Author

Seiichi Manyama, Nov 30 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A052868, A362775, A367790.

Cf. A091695, A360100.

Programs

Maple

A367789 := proc(n)
    n!*add((k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!,k=0..n) ;
end proc:
seq(A367789(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))))

Formula

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

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