A298249 Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(2*k+1)/6)).

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

Offset

0

Comments

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

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} (1 - x^A000330(k)).

Mathematica

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

Crossrefs

Cf. A000330, A276516, A279220, A298246, A298247.

Sequence in context: A267152 A151667 A241759 * A286993 A015274 A011651

Adjacent sequences: A298246 A298247 A298248 * A298250 A298251 A298252

Keyword

sign

Author

Ilya Gutkovskiy, Jan 15 2018

Status

approved