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A298247 Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(k+2)/6)).

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%I A298247 #6 Feb 16 2025 08:33:53
%S A298247 1,-1,0,0,-1,1,0,0,0,0,-1,1,0,0,1,-1,0,0,0,0,-1,1,0,0,1,-1,0,0,0,0,1,
%T A298247 -1,0,0,-1,0,1,0,0,1,-1,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,1,-2,1,0,-1,2,
%U A298247 -1,0,0,0,-1,2,-1,0,1,-2,1,0,0,0,0,1,-1,0,0,-1,1,0,0,-1,1,-1,1,1,-1,1,0,-1,0,1,-2,1,0,-1,1,0,-1,1,0,1
%N A298247 Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(k+2)/6)).
%C A298247 The difference between the number of partitions of n into an even number of distinct tetrahedral numbers and the number of partitions of n into an odd number of distinct tetrahedral numbers.
%H A298247 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H A298247 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A298247 G.f.: Product_{k>=1} (1 - x^A000292(k)).
%t A298247 nmax = 104; CoefficientList[Series[Product[1 - x^(k (k + 1) (k + 2)/6), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A298247 Cf. A000292, A068980, A279278, A292518, A298249.
%K A298247 sign
%O A298247 0,57
%A A298247 _Ilya Gutkovskiy_, Jan 15 2018