A379932 E.g.f. A(x) satisfies A(x) = ( exp(-x) + x*A(x) )^2.

1, 0, 2, 10, 88, 978, 13468, 221338, 4233584, 92458018, 2271283684, 62012911530, 1863436238728, 61124896911154, 2173660174175228, 83304031307483962, 3423089366607304672, 150143469737701318722, 7001969736087834197716, 345972733119776006045386

Offset: 0

Author

Seiichi Manyama, Jan 06 2025

Keywords

• nonn

Crossrefs

Cf. A379866, A379937.

Cf. A130102, A379879.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(4*exp(-2*x)/(1+sqrt(1-4*x*exp(-x)))^2))

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379879.

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