A373221 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 7^j)).

1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 14, 18, 22, 28, 34, 41, 50, 60, 72, 86, 105, 124, 146, 174, 204, 240, 282, 332, 386, 450, 524, 606, 703, 812, 940, 1082, 1243, 1428, 1636, 1873, 2140, 2448, 2788, 3172, 3610, 4096, 4646, 5264, 5963, 6737, 7607, 8584, 9668, 10887, 12244, 13765, 15451, 17328

Offset: 0

Author

Seiichi Manyama, May 28 2024

Keywords

• nonn

Comments

This sequence is different from A093950. The first difference occurs at a(50) = 6737, whereas A093950(50) = 6736.

Crossrefs

Cf. A000041, A174065, A327726, A373219, A373220.

Cf. A000009, A093950, A373217.

Programs

PARI

my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1+x^k)^(valuation(k, 7)+1)))

Formula

G.f.: Product_{k>=1} (1 + x^k)^A373217(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^7).