A081718 Array T(m,n) read by antidiagonals, where T(m,n) = number of m X infinity multiplicity integer partition (mip) matrix of n (m >= 0, n >= 0).

1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 3, 1, 0, 1, 1, 4, 6, 5, 1, 0, 1, 1, 5, 10, 13, 7, 1, 0, 1, 1, 6, 15, 26, 23, 11, 1, 0, 1, 1, 7, 21, 45, 55, 44, 15, 1, 0, 1, 1, 8, 28, 71, 110, 121, 74, 22, 1, 0, 1, 1, 9, 36, 105, 196, 271, 237, 129, 30, 1, 0, 1, 1, 10, 45, 148, 322, 532

Offset

0,13

Comments

For n > 0, the n-th column is given by a polynomial of degree n-1. - David Wasserman, Jun 21 2004

Links

Table of n, a(n) for n=0..84.

W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(1-3), July 2000, 235-245.

Formula

There is a recurrence involving the partition function.

Example

Array begins:
1 1 0 0 0 ...
1 1 1 1 1 ...
1 1 2 3 5 ...
1 1 3 6 13 ...

Crossrefs

Rows and columns give A022811, A022812, A022813, A022814, A022815, etc.

Sequence in context: A192517 A309896 A083856 * A290353 A263857 A334895

Adjacent sequences: A081715 A081716 A081717 * A081719 A081720 A081721

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Apr 05 2003

Extensions

More terms from David Wasserman, Jun 21 2004

Status

approved