A292519 - OEIS

%I #8 Jul 14 2018 02:51:30

%S 1,-1,1,-2,2,-2,2,-2,2,-2,1,-1,2,-1,1,-3,3,-3,4,-4,5,-6,5,-6,8,-6,6,

%T -8,6,-6,7,-5,6,-7,5,-7,9,-7,9,-11,9,-11,13,-10,12,-15,12,-14,16,-13,

%U 15,-15,11,-14,15,-11,15,-18,15,-19,23,-21,25,-27,24,-28,28,-24,28,-29,24,-28,31,-25,29,-33,30,-35,36,-35,42

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

%C Convolution inverse of A024940.

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

%H Seiichi Manyama, <a href="/A292519/b292519.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%t nmax = 80; CoefficientList[Series[Product[1/(1 + x^(k (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A007294, A024940, A280366, A292518.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Sep 18 2017