

A119271


Triangle: number of exactly (m1)dimensional partitions of n, for n >= 1, m >= 0.


3



1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 5, 6, 1, 0, 1, 9, 18, 10, 1, 0, 1, 13, 44, 49, 15, 1, 0, 1, 20, 97, 172, 110, 21, 1, 0, 1, 28, 195, 512, 550, 216, 28, 1, 0, 1, 40, 377, 1370, 2195, 1486, 385, 36, 1, 0, 1, 54, 694, 3396, 7603, 7886, 3514, 638, 45, 1, 0, 1, 75, 1251, 7968
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OFFSET

1,9


COMMENTS

The partition of 1 is considered to be dimension 1 by convention.


LINKS

Suresh Govindarajan, Rows n = 1..26 of Triangle
Suresh Govindarajan, Partitions Generator (gives partitions of integers <= 25 in any dimension using this triangle).
Suresh Govindarajan, Refined counting of higherdimensional partitions
Suresh Govindarajan, Notes on higherdimensional partitions, arXiv preprint arXiv:1203.4419, 2012.


FORMULA

a(n,m) = A096806(n,m1)a(n,m1). Binomial transform of nth row lists the (m1) dimensional partitions of n.


EXAMPLE

Table starts:
1,
0,1,
0,1,1,
0,1,3,1,
0,1,5,6,1,


CROSSREFS

Cf. A119270, A096806. Column 1 is A007042.
Sequence in context: A081719 A327618 A121314 * A323222 A125104 A098157
Adjacent sequences: A119268 A119269 A119270 * A119272 A119273 A119274


KEYWORD

nonn,tabl,hard


AUTHOR

Franklin T. AdamsWatters, May 11 2006


STATUS

approved



