A339352 G.f.: Product_{k>=1} (1 + (-x)^(k^2) / (1 + x^k)).

1, -1, 1, -1, 2, -2, 1, -1, 2, -3, 2, -2, 4, -5, 4, -4, 7, -8, 7, -7, 9, -10, 8, -8, 11, -14, 13, -13, 16, -18, 17, -16, 19, -22, 23, -23, 26, -29, 29, -30, 34, -38, 38, -39, 44, -48, 47, -48, 56, -64, 65, -66, 75, -82, 80, -80, 90, -99, 98, -100, 114

Offset

0,5

Comments

The difference between the number of partitions of n into an even number of parts where every part k appears at least k times and the number of partitions of n into an odd number of parts where every part k appears at least k times.

Links

Table of n, a(n) for n=0..60.

Mathematica

nmax = 60; CoefficientList[Series[Product[1 + (-x)^(k^2)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A081362, A117144.

Sequence in context: A066030 A025863 A346307 * A372515 A305825 A366780

Adjacent sequences: A339349 A339350 A339351 * A339353 A339354 A339355

Keyword

sign

Author

Ilya Gutkovskiy, Dec 01 2020

Status

approved