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%I #19 Sep 23 2020 03:21:26
%S 1,1,2,4,11,29,94,304,1005,3336,11398,38739,132340,451086,1541074,
%T 5242767,17779666,60048847,202124143,677000711,2256910444,7486274436,
%U 24713275977,81162110629,265192045408,862061443031,2788194736946,8972104829849,28726271274133,91515498561954,290116750935925
%N Number of partitions of the n-th tetrahedral number into tetrahedral numbers.
%H David A. Corneth, <a href="/A298269/b298269.txt">Table of n, a(n) for n = 0..500</a>
%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 related partition-counting sequences</a>
%F a(n) = [x^A000292(n)] Product_{k>=1} 1/(1 - x^A000292(k)).
%F a(n) = A068980(A000292(n)).
%e a(3) = 4 because third tetrahedral number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t Table[SeriesCoefficient[Product[1/(1 - x^(k (k + 1) (k + 2)/6)), {k, 1, n}], {x, 0, n (n + 1) (n + 2)/6}], {n, 0, 30}]
%Y Cf. A000292, A037444, A068980, A072964, A298857.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 27 2018