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%I #15 Nov 20 2020 15:45:09
%S 1,1,0,0,0,1,2,5,5,20,35,75,154,336,730,1570,3394,7339,16085,35015,
%T 76269,164821,359704,782004,1696804,3668860,7953962,17184203,37093184,
%U 79825297,171824175,368838299,790404448,1690297309,3610816466,7696144659,16374004711,34766160358
%N Number of partitions of the n-th tetrahedral number into exactly n positive tetrahedral numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = [x^A000292(n) y^n] Product_{j>=1} 1 / (1 - y*x^A000292(j)).
%e The 6th tetrahedral number is 56 and 56 = 1 + 1 + 4 + 10 + 20 + 20 = 4 + 4 + 4 + 4 + 20 + 20, so a(6) = 2.
%Y Cf. A000292, A068980, A298269, A298857, A303170, A307643, A338585, A338778.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Nov 08 2020