A327851 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A111374.

1, 1, 2, 2, 4, 4, 6, 8, 12, 15, 19, 24, 30, 36, 47, 57, 74, 88, 112, 130, 160, 190, 232, 277, 333, 399, 471, 554, 656, 768, 908, 1060, 1256, 1452, 1702, 1968, 2294, 2646, 3068, 3549, 4093, 4710, 5418, 6211, 7121, 8138, 9331, 10625, 12150, 13817, 15749, 17858, 20290, 23000, 26054

Offset

0,3

Comments

a(n) > 0.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{i>=1} Product_{j>=1} (1-x^(i*(8*j-3))) * (1-x^(i*(8*j-5))) / ((1-x^(i*(8*j-1))) * (1-x^(i*(8*j-7)))).

G.f.: Product_{k>=1} (1-x^k)^(-A035185(k)).

Mathematica

nmax = 60; CoefficientList[Series[Product[QPochhammer[x^(8*j - 3)] * QPochhammer[x^(8*j - 5)]/(QPochhammer[x^(8*j - 7)] * QPochhammer[x^(8*j - 1)]), {j, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 28 2019 *)

Prog

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^sumdiv(k, d, kronecker(2, d))))

Crossrefs

Convolution inverse of A327852.

Product_{k>=1} (1 - x^k)^(- Sum_{d|k} (b/d)), where (m/n) is the Kronecker symbol: this sequence (b=2), A107742 (b=4), A327716 (b=5).

Cf. A035185, A111374.

Sequence in context: A264393 A362307 A094858 * A029940 A045674 A276065

Adjacent sequences: A327848 A327849 A327850 * A327852 A327853 A327854

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2019

Status

approved