A300575 Coefficient of x^n in (1+x)(1-x^3)(1+x^5)(1-x^7)(1+x^9)...

1, 1, 0, -1, -1, 1, 1, -1, -2, 0, 2, 0, -3, -1, 3, 2, -3, -3, 3, 4, -3, -6, 2, 7, -1, -8, 0, 10, 2, -11, -4, 12, 7, -13, -10, 13, 13, -13, -17, 13, 22, -11, -26, 9, 31, -6, -36, 2, 41, 3, -46, -9, 51, 17, -55, -26, 59, 36, -62, -48, 63, 61, -64, -75, 64, 92, -60, -109, 55, 127, -48, -147, 37, 167

Offset: 0

Author

Gus Wiseman, Mar 09 2018

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A000009, A010815, A027193, A067659, A078408, A081362, A220418, A290261, A292043, A292137, A300574.

Programs

Mathematica

CoefficientList[Series[QPochhammer[-x,-x^2],{x,0,100}],x]

Formula

O.g.f.: Product_{n >= 0} (1 + (-1)^n x^(2n+1)).

a(n) = Sum (-1)^k where the sum is over all strict integer partitions of n into odd parts and k is the number of parts not congruent to 1 modulo 4.