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A298269 Number of partitions of the n-th tetrahedral number into tetrahedral numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

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

Cf. A000292, A037444, A068980, A072964, A298857.

Sequence in context: A052831 A148146 A148147 * A148148 A148149 A034769

Adjacent sequences:  A298266 A298267 A298268 * A298270 A298271 A298272

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 27 2018

STATUS

approved

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Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)