A372251 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^2 * (1 + A(x))/2 ).

1, 1, 6, 73, 1364, 34586, 1110496, 43207004, 1976199792, 103925934712, 6178846168976, 409847155094840, 30007066358487040, 2403751529017358144, 209131503815967330816, 19637892118783264231936, 1979605910448187576510208, 213226210180592877512104832

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) ~ sqrt((1 + s)/(4 + 9*s)) * s^(2*n + 1) * (2 + 3*s)^n * n^(n-1) / (2^n * exp(n)), where s = 1.470103625022272111740158699814771551850270522048... is the root of the equation log(s) = (1 + s)/(2 + 3*s). - Vaclav Kotesovec, Apr 24 2024

Prog

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

Crossrefs

Cf. A138860, A372246.

Sequence in context: A202557 A041060 A089926 * A135594 A346960 A168603

Adjacent sequences: A372248 A372249 A372250 * A372252 A372253 A372254

Keyword

nonn

Author

Seiichi Manyama, Apr 24 2024

Status

approved