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A298269
Number of partitions of the n-th tetrahedral number into tetrahedral numbers.
6
1, 1, 2, 4, 11, 29, 94, 304, 1005, 3336, 11398, 38739, 132340, 451086, 1541074, 5242767, 17779666, 60048847, 202124143, 677000711, 2256910444, 7486274436, 24713275977, 81162110629, 265192045408, 862061443031, 2788194736946, 8972104829849, 28726271274133, 91515498561954, 290116750935925
OFFSET
0,3
FORMULA
a(n) = [x^A000292(n)] Product_{k>=1} 1/(1 - x^A000292(k)).
a(n) = A068980(A000292(n)).
EXAMPLE
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].
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 27 2018
STATUS
approved