A298247 Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(k+2)/6)).

1, -1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -2, 1, 0, -1, 2, -1, 0, 0, 0, -1, 2, -1, 0, 1, -2, 1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, -1, 1, -1, 1, 1, -1, 1, 0, -1, 0, 1, -2, 1, 0, -1, 1, 0, -1, 1, 0, 1

Offset: 0

Author

Ilya Gutkovskiy, Jan 15 2018

Keywords

• sign

Comments

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

Links

• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000292, A068980, A279278, A292518, A298249.

Programs

Mathematica

nmax = 104; CoefficientList[Series[Product[1 - x^(k (k + 1) (k + 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 - x^A000292(k)).