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A298247
Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(k+2)/6)).
1
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
0,57
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.
FORMULA
G.f.: Product_{k>=1} (1 - x^A000292(k)).
MATHEMATICA
nmax = 104; CoefficientList[Series[Product[1 - x^(k (k + 1) (k + 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 15 2018
STATUS
approved