A377599 E.g.f. satisfies A(x) = exp( x * A(x) / (1-x)^2 ) / (1-x).

1, 2, 13, 145, 2277, 46461, 1172713, 35374697, 1243296169, 49940748073, 2258238723021, 113567169318285, 6289161888870061, 380364426242671469, 24948313525570134001, 1764095427822803465521, 133782341347522663175889, 10832097536377585282160337, 932693691617428946786304661

Offset: 0

Author

Seiichi Manyama, Nov 14 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A367789, A377608, A377811.

Cf. A361599.

Programs

PARI

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

PARI

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

Formula

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

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