A294395 E.g.f.: exp(Sum_{n>=1} A050999(n) * x^n).

1, 1, 3, 67, 289, 5121, 71731, 861043, 18134817, 303946849, 6724342531, 146426154051, 3533373668353, 93259190078497, 2489644674735219, 75193364720030131, 2265438714279130561, 74716734198386887233, 2543592184722884351107, 90853513680763023292099

Offset: 0

Author

Seiichi Manyama, Oct 30 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..422

Crossrefs

E.g.f.: exp(Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294392 (k=0), A294394 (k=1), this sequence (k=2).

Cf. A050999, A262811.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, d^2*(d%2))*x^k))))

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A050999(k)*a(n-k)/(n-k)! for n > 0.

a(n) ~ (3*zeta(3))^(1/8) * n^(n - 1/8) / (2*exp(n - 4*zeta(3)^(1/4) * n^(3/4) / 3^(3/4) - n^(1/4) / (4*3^(5/4)*zeta(3)^(1/4)))). - Vaclav Kotesovec, Nov 01 2024