A292519 Expansion of Product_{k>=1} 1/(1 + x^(k*(k+1)/2)).

1, -1, 1, -2, 2, -2, 2, -2, 2, -2, 1, -1, 2, -1, 1, -3, 3, -3, 4, -4, 5, -6, 5, -6, 8, -6, 6, -8, 6, -6, 7, -5, 6, -7, 5, -7, 9, -7, 9, -11, 9, -11, 13, -10, 12, -15, 12, -14, 16, -13, 15, -15, 11, -14, 15, -11, 15, -18, 15, -19, 23, -21, 25, -27, 24, -28, 28, -24, 28, -29, 24, -28, 31, -25, 29, -33, 30, -35, 36, -35, 42

Offset: 0

Author

Ilya Gutkovskiy, Sep 18 2017

Keywords

• sign

Comments

Convolution inverse of A024940.

The difference between the number of partitions of n into an even number of triangular numbers and the number of partitions of n into an odd number of triangular numbers.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for related partition-counting sequences

Crossrefs

Cf. A007294, A024940, A280366, A292518.

Programs

Mathematica

nmax = 80; CoefficientList[Series[Product[1/(1 + x^(k (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 + x^(k*(k+1)/2)).