A356540 Expansion of e.g.f. Product_{k>0} 1/(1 - (3 * x)^k)^(1/3^k).

1, 1, 6, 40, 496, 5400, 114400, 1760080, 47671680, 1090230400, 34312096000, 916877068800, 39605683532800, 1211405062067200, 55580939301888000, 2260295506653184000, 115398744818925568000, 4928605977341190144000, 305987190350116667392000

Offset: 0

Author

Seiichi Manyama, Aug 11 2022

Keywords

• nonn

Crossrefs

Cf. A000041, A006950, A356530, A356538.

Cf. A356539.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(3*x)^k)^(1/3^k))))

PARI

a356539(n) = sumdiv(n, d, d*3^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356539(j)*v[i-j+1]/(i-j)!)); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A356539(k) * a(n-k)/(n-k)!.