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A298857 Number of partitions of the n-th tetrahedral number into distinct tetrahedral numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..53.

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 + 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

Cf. A000292, A030273, A279278, A288126, A298269.

Sequence in context: A133091 A112204 A129710 * A070680 A054711 A241424

Adjacent sequences:  A298854 A298855 A298856 * A298858 A298859 A298860

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 27 2018

STATUS

approved

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Last modified August 8 01:57 EDT 2020. Contains 336287 sequences. (Running on oeis4.)