|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
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
|
|
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: A339834 A148146 A148147 * A148148 A148149 A034769
Adjacent sequences: A298266 A298267 A298268 * A298270 A298271 A298272
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ilya Gutkovskiy, Jan 27 2018
|
|
STATUS
|
approved
|
|
|
|