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A292518 Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)). 8
1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, -1, 2, -1, 1, -2, 1, 0, 0, 0, 0, 1, -1, 1, -3, 2, -1, 2, -1, 0, 1, -1, 0, -2, 3, -1, 1, -2, 1, 1, -2, 0, 0, 2, 0, -1, 0, 2, -2, -1, -1, 1, 2, -1, 1, -1, 1, -2, 1, -2, 3, 1, -2, 0, -2, 3, -1, -1, 0, 3, -1, 0, -2, 1, 0, -3, 2, 2, 1, -1, -1, 0, 0, -1, 0, 2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Convolution inverse of A007294.

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

Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054. - Gus Wiseman, Oct 22 2018

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for related partition-counting sequences

FORMULA

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

MATHEMATICA

nmax = 90; CoefficientList[Series[Product[1 - x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Product_{k>=1} (1 - x^(k*((m-2)*k-(m-4))/2)): this sequence (m=3), A276516 (m=4), A305355 (m=5).

Cf. A007294, A010054, A024940, A280366, A320767, A320784.

Sequence in context: A187360 A334368 A240718 * A264997 A222759 A024940

Adjacent sequences:  A292515 A292516 A292517 * A292519 A292520 A292521

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Sep 18 2017

STATUS

approved

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Last modified April 15 03:00 EDT 2021. Contains 342974 sequences. (Running on oeis4.)