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A096751 Square table, read by antidiagonals, where T(n,k) equals the number of n-dimensional partitions of k. 12
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 5, 1, 1, 1, 5, 10, 13, 7, 1, 1, 1, 6, 15, 26, 24, 11, 1, 1, 1, 7, 21, 45, 59, 48, 15, 1, 1, 1, 8, 28, 71, 120, 140, 86, 22, 1, 1, 1, 9, 36, 105, 216, 326, 307, 160, 30, 1, 1, 1, 10, 45, 148, 357, 657, 835, 684, 282, 42, 1, 1, 1, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Main diagonal forms A096752. Antidiagonal sums form A096753. Row with index n lists the row sums of the n-th matrix power of triangle A096651, for n>=0.

REFERENCES

G. E. Andrews, The Theory of Partitions, Add.-Wes. 1976, pp. 189-197.

LINKS

Table of n, a(n) for n=0..80.

A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]

FORMULA

T(0, n)=T(n, 0)=T(n, 1)=1 for n>=0.

Inverse binomial transforms of the columns is given by triangle A096806.

EXAMPLE

n-th row lists n-dimensional partitions; table begins with n=0:

[1,1,1,1,1,1,1,1,1,1,1,1,...],

[1,1,2,3,5,7,11,15,22,30,42,56,...],

[1,1,3,6,13,24,48,86,160,282,500,859,...],

[1,1,4,10,26,59,140,307,684,1464,3122,...],

[1,1,5,15,45,120,326,835,2145,5345,...],

[1,1,6,21,71,216,657,1907,5507,15522,...],

[1,1,7,28,105,357,1197,3857,12300,38430,...],

[1,1,8,36,148,554,2024,7134,24796,84625,...],

[1,1,9,45,201,819,3231,12321,46209,170370,...],

[1,1,10,55,265,1165,4927,20155,80920,...],...

CROSSREFS

Cf. A096651, A096752, A096753.

Cf. A096806.

Cf. A042984.

Sequence in context: A208891 A047030 A047120 * A099233 A133815 A130580

Adjacent sequences:  A096748 A096749 A096750 * A096752 A096753 A096754

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 07 2004

STATUS

approved

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Last modified March 28 07:53 EDT 2017. Contains 284182 sequences.