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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).
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%I #8 Oct 19 2016 16:05:45

%S 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,

%T 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,

%U 121,74,22,1,0,1,1,9,36,105,196,271,237,129,30,1,0,1,1,10,45,148,322,532

%N 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).

%C For n > 0, the n-th column is given by a polynomial of degree n-1. - _David Wasserman_, Jun 21 2004

%H W. C. Yang, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00412-4">Derivatives are essentially integer partitions</a>, Discrete Mathematics, 222(1-3), July 2000, 235-245.

%F There is a recurrence involving the partition function.

%e Array begins:

%e 1 1 0 0 0 ...

%e 1 1 1 1 1 ...

%e 1 1 2 3 5 ...

%e 1 1 3 6 13 ...

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

%K nonn,tabl,easy

%O 0,13

%A _N. J. A. Sloane_, Apr 05 2003

%E More terms from _David Wasserman_, Jun 21 2004