A379936 E.g.f. A(x) satisfies A(x) = 1/( exp(-x*A(x)^(1/2)) - x )^2.

1, 4, 30, 344, 5400, 108492, 2667952, 77811120, 2629399680, 101122817300, 4363964377344, 208925612290056, 10992411683169280, 630611992509716700, 39182624685283891200, 2621745777377998537568, 187969244952968687812608, 14377545994804829244970020

Offset: 0

Author

Seiichi Manyama, Jan 06 2025

Keywords

• nonn

Crossrefs

Cf. A379933, A379934.

Cf. A088690.

Programs

PARI

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

PARI

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

Formula

E.g.f.: ( (1/x) * Series_Reversion( x*exp(-x)/(1+x) ) )^2.

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A088690.

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