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A298857
Number of partitions of the n-th tetrahedral number into distinct tetrahedral numbers.
5
1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 5, 5, 10, 12, 17, 15, 22, 30, 56, 65, 72, 92, 172, 219, 299, 368, 478, 810, 1055, 1508, 1778, 2277, 3815, 5214, 7103, 8615, 11614, 18079, 24428, 33704, 42877, 56639, 85597, 116984, 159179, 199356, 268965, 400612, 545674, 740356, 950897, 1261597, 1842307
OFFSET
0,6
FORMULA
a(n) = [x^A000292(n)] Product_{k>=1} (1 + x^A000292(k)).
a(n) = A279278(A000292(n)).
EXAMPLE
a(5) = 2 because fifth tetrahedral number is 35 and we have [35] and [20, 10, 4, 1].
MATHEMATICA
Table[SeriesCoefficient[Product[1 + x^(k (k + 1) (k + 2)/6), {k, 1, n}], {x, 0, n (n + 1) (n + 2)/6}], {n, 0, 53}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 27 2018
STATUS
approved