A381999 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^3.

1, 1, 10, 156, 3656, 115400, 4595232, 221281312, 12510826624, 812633118336, 59642105050880, 4881685773730304, 440905471531302912, 43559980305765793792, 4673231270870843441152, 541042726968231082967040, 67236501012517546330062848, 8927220151967826907452440576

Offset: 0

Author

Seiichi Manyama, Mar 12 2025

Keywords

• nonn

Crossrefs

Cf. A336950, A381997, A381998, A382000, A382001.

Cf. A001764, A364983, A371318.

Programs

PARI

a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(3*k+1, k)/((3*k+1)*(n-k)!));

Formula

a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A001764(k)/(n-k)!.

a(n) ~ sqrt(3*(1 + LambertW(8/27))) * 2^(n - 3/2) * n^(n-1) / (exp(n) * LambertW(8/27)^n). - Vaclav Kotesovec, Mar 22 2025