OFFSET
0,9
COMMENTS
The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.
A(n,k) is the number of n-uniform k-block sets of multisets.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
FORMULA
EXAMPLE
Array begins:
====================================================================
n\k | 0 1 2 3 4 5
----+---------------------------------------------------------------
0 | 1 1 0 0 0 0 ...
1 | 1 1 1 1 1 1 ...
2 | 1 2 12 124 1800 33648 ...
3 | 1 4 124 10596 1764244 484423460 ...
4 | 1 8 1280 930880 1849386640 7798297361808 ...
5 | 1 16 13456 85835216 2098356708016 140094551934813712 ...
6 | 1 32 143808 8206486848 2516779512105152 ...
...
The A(2,2) matrices are:
[1 0] [1 0] [1 0] [2 0] [1 1] [1 0]
[1 0] [0 1] [0 1] [0 1] [1 0] [1 1]
[0 1] [1 0] [0 1] [0 1] [0 1] [0 1]
[0 1] [0 1] [1 0]
.
[1 0] [1 0] [1 0] [2 1] [2 0] [1 0]
[1 0] [0 2] [0 1] [0 1] [0 2] [1 2]
[0 2] [1 0] [1 1]
PROG
(PARI) T(n, k)={my(m=n*k); sum(j=0, m, binomial(binomial(j+n-1, n), k)*sum(i=j, m, (-1)^(i-j)*binomial(i, j)))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 13 2020
STATUS
approved