OFFSET
0,8
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
FORMULA
A(n,k) = binomial(binomial(n + k - 1, n) + n - 1, n).
EXAMPLE
Array begins:
==================================================================
n\k | 0 1 2 3 4 5 6
----+-------------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 0 1 2 3 4 5 6 ...
2 | 0 1 6 21 55 120 231 ...
3 | 0 1 20 220 1540 7770 30856 ...
4 | 0 1 70 3060 73815 1088430 11009376 ...
5 | 0 1 252 53130 5461512 286243776 8809549056 ...
6 | 0 1 924 1107568 581106988 127860662755 13949678575756 ...
...
The A(2,2) = 6 multisets are:
{{1,1}, {1,1}},
{{1,1}, {1,2}},
{{1,1}, {2,2}},
{{1,2}, {1,2}},
{{1,2}, {2,2}},
{{2,2}, {2,2}}.
PROG
(PARI) T(n, k)={binomial(binomial(n + k - 1, n) + n - 1, n)}
{ for(n=0, 7, for(k=0, 7, print1(T(n, k), ", ")); print) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 17 2020
STATUS
approved