A373220 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 6^j)).

1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 12, 15, 20, 24, 29, 37, 44, 53, 67, 79, 94, 115, 135, 160, 193, 226, 265, 315, 367, 428, 505, 585, 678, 792, 913, 1054, 1225, 1406, 1614, 1862, 2129, 2436, 2797, 3187, 3630, 4147, 4709, 5347, 6084, 6887, 7793, 8832, 9968, 11247, 12706, 14301, 16089, 18116, 20337

Offset: 0

Author

Seiichi Manyama, May 28 2024

Keywords

• nonn

Crossrefs

Cf. A000041, A174065, A327726, A373219, A373221.

Cf. A000009, A373216.

Programs

PARI

my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(valuation(k, 6)+1)))

Formula

G.f.: Product_{k>=1} (1 + x^k)^A373216(k).

Let A(x) be the g.f. of this sequence, and B(x) be the g.f. of A000009, then B(x) = A(x)/A(x^6).