A362696 Expansion of e.g.f. Product_{k>0} (1 - x^(3*k-2))^(-1/(3*k-2)).

1, 1, 2, 6, 30, 150, 900, 7020, 62460, 562140, 5984280, 67252680, 863165160, 11700148680, 173098134000, 2625661170000, 45310413258000, 782198417206800, 14310269286746400, 280333959468789600, 6002139207488767200, 129820528515538159200, 2934651197018947982400

Offset: 0

Author

Seiichi Manyama, Jul 07 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A001817, A035382, A206303, A262947, A362697.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1,N, (1-x^(3*k-2))^(1/(3*k-2)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A001817(k) * a(n-k)/(n-k)!.