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A298269
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Number of partitions of the n-th tetrahedral number into tetrahedral numbers.
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6
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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
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OFFSET
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0,3
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LINKS
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David A. Corneth, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Tetrahedral Number
Index to sequences related to pyramidal numbers
Index entries for related partition-counting sequences
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FORMULA
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a(n) = [x^A000292(n)] Product_{k>=1} 1/(1 - x^A000292(k)).
a(n) = A068980(A000292(n)).
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EXAMPLE
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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].
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000292, A037444, A068980, A072964, A298857.
Sequence in context: A339834 A148146 A148147 * A148148 A148149 A034769
Adjacent sequences: A298266 A298267 A298268 * A298270 A298271 A298272
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jan 27 2018
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STATUS
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approved
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