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Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)).
10

%I #14 Oct 26 2018 18:32:50

%S 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,

%T 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,

%U -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

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

%C Convolution inverse of A007294.

%C 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.

%C Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054. - _Gus Wiseman_, Oct 22 2018

%H Seiichi Manyama, <a href="/A292518/b292518.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

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

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

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

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

%K sign

%O 0,11

%A _Ilya Gutkovskiy_, Sep 18 2017