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

%I #42 Jul 07 2023 14:57:04

%S 1,1,2,6,30,150,900,7020,62460,562140,5984280,67252680,863165160,

%T 11700148680,173098134000,2625661170000,45310413258000,

%U 782198417206800,14310269286746400,280333959468789600,6002139207488767200,129820528515538159200,2934651197018947982400

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

%H Seiichi Manyama, <a href="/A362696/b362696.txt">Table of n, a(n) for n = 0..449</a>

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

%o (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)))))

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

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 07 2023