%I #43 Jul 07 2023 14:57:00
%S 1,0,1,0,9,24,225,504,16065,27216,1555281,6123600,159249321,779262120,
%T 31816914129,240363179784,8207359913025,66059979227424,
%U 2145292484152545,19782668403572256,1015331126023222281,7961977144683689400,454920488042137314561
%N Expansion of e.g.f. Product_{k>0} (1 - x^(3*k-1))^(-1/(3*k-1)).
%H Seiichi Manyama, <a href="/A362697/b362697.txt">Table of n, a(n) for n = 0..449</a>
%F a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A001822(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-1))^(1/(3*k-1)))))
%Y Cf. A001822, A035386, A206303, A262946, A362696.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Jul 07 2023