A284321 Expansion of Product_{k>=0} (1 - x^(5*k+1))*(1 - x^(5*k+4)) in powers of x.

1, -1, 0, 0, -1, 1, -1, 1, 0, -1, 2, -2, 1, 1, -2, 3, -3, 2, 0, -3, 5, -5, 3, 1, -5, 7, -7, 4, 1, -7, 11, -11, 6, 2, -10, 15, -15, 9, 2, -14, 22, -22, 12, 4, -20, 30, -29, 17, 4, -27, 42, -41, 23, 7, -37, 55, -54, 31, 8, -49, 76, -74, 41, 12, -66, 99, -96, 55, 14

Offset: 0

Author

Seiichi Manyama, Mar 25 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003114, A284150, A284322, A284314, A284317.

Cf. Product_{k>=0} (1 - x^(m*k+1))*(1 - x^(m*k+m-1)): A137569 (m=3), A081362 (m=4), this sequence (m=5), A109389 (m=6).

Programs

Mathematica

CoefficientList[Series[Product[(1 - x^(5k + 1)) ( 1 - x^(5k + 4)), {k, 0, 100}], {x, 0, 100}],x] (* Indranil Ghosh, Mar 25 2017 *)

PARI

Vec(prod(k=0, 100, (1 - x^(5*k + 1)) * (1 - x^(5*k + 4))) + O(x^101)) \\ Indranil Ghosh, Mar 25 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} A284150(k)*a(n-k), a(0) = 1.