%I #8 Mar 23 2021 15:52:31
%S 1,0,0,1,0,0,1,0,0,2,0,0,2,0,0,2,0,0,3,1,0,3,1,0,3,1,0,4,2,0,4,2,0,4,
%T 3,0,5,4,1,5,4,1,5,5,1,6,6,2,6,6,2,6,7,3,7,9,4,8,9,4,8,10,5,9,12,6,10,
%U 12,7,10,13,8,12,15,10,13,16,11,13,17,12
%N Number of partitions of 2*n into exactly n nonzero tetrahedral numbers.
%H David A. Corneth, <a href="/A341773/b341773.txt">Table of n, a(n) for n = 0..2999</a>
%F G.f.: Product_{k>=0} 1 / (1 - x^(binomial(k+4,3)-1)).
%t nmax = 80; CoefficientList[Series[Product[1/(1 - x^(Binomial[k + 4, 3] - 1)), {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000292, A024692, A062748, A068980, A298269, A319799, A338586, A341774, A341775, A341776, A341777, A341778.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Feb 19 2021