A327688 Expansion of Product_{k>=1} B(x^k), where B(x) is the g.f. of A007325.

1, -1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -2, 2, 1, 0, 1, -1, -1, -1, -1, 2, 1, 0, 1, -1, -3, 1, 2, -1, 0, 4, -6, -2, 3, -1, 1, 4, -1, -2, -1, 2, -4, 4, 0, -3, 1, -3, 4, 2, -1, 3, -1, -3, -1, 2, -3, 1, 2, -6, -3, 12, -7, 3, 11, -7, -4, 7, -10, -1, 7, 2, -16, 11, 2, -10, 14, -4, 3, -3

Offset

0,12

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction.

Formula

G.f.: Product_{i>=1} Product_{j>=1} (1-x^(i*(5*j-1))) * (1-x^(i*(5*j-4))) / ((1-x^(i*(5*j-2))) * (1-x^(i*(5*j-3)))).

G.f.: Product_{k>=1} (1-x^k)^A035187(k).

Prog

(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^k)^sumdiv(k, d, kronecker(5, d))))

Crossrefs

Cf. A007325, A035187, A307757, A327686, A327690, A327691, A327716.

Sequence in context: A016385 A189996 A016390 * A055800 A060572 A163543

Adjacent sequences: A327685 A327686 A327687 * A327689 A327690 A327691

Keyword

sign,look

Author

Seiichi Manyama, Sep 22 2019

Status

approved