A327852 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A092869.

1, -1, -1, 1, -1, 1, 1, -3, 1, 2, 0, 2, -2, -2, -1, 3, 1, -5, 2, 0, 0, 8, -4, -7, 5, -2, 0, 1, -8, 0, 12, 2, -3, -1, -7, 9, 4, -7, -7, -6, 10, 9, 2, -6, -14, 15, 3, -15, 19, -30, 6, 37, -31, 10, 9, -23, 20, 4, -29, 4, 14, 4, -13, 23, -14, -19, 39, -29, -23, 35, 0, -34, 48

Offset

0,8

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-1))) * (1-x^(i*(8*j-7))) / ((1-x^(i*(8*j-3))) * (1-x^(i*(8*j-5)))).

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

Prog

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

Crossrefs

Product_{k>=1} (1 - x^k)^(Sum_{d|k} (b/d)), where (m/n) is the Kronecker symbol: this sequence (b=2), A288007 (b=4), A327688 (b=5).

Cf. A035185, A092869, A327851.

Sequence in context: A211358 A211356 A176107 * A190561 A359793 A074735

Adjacent sequences: A327849 A327850 A327851 * A327853 A327854 A327855

Keyword

sign

Author

Seiichi Manyama, Sep 28 2019

Status

approved