A331436 Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 6, 1, 0, 1, 4, 21, 20, 1, 0, 1, 5, 55, 220, 70, 1, 0, 1, 6, 120, 1540, 3060, 252, 1, 0, 1, 7, 231, 7770, 73815, 53130, 924, 1, 0, 1, 8, 406, 30856, 1088430, 5461512, 1107568, 3432, 1, 0, 1, 9, 666, 102340, 11009376, 286243776, 581106988, 26978328, 12870, 1, 0

Offset: 0

Author

Andrew Howroyd, Jan 17 2020

Keywords

• nonn
• tabl

Examples

			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}}.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325

Crossrefs

Rows n=0..3 are A000012, A001477, A002817, A140236.

Columns k=0..10 are A000007, A000012, A000984, A099121, A099122, A099123, A099124, A099125, A099126, A099127, A099128.

Min diagonal is A331477.

Programs

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) }

Formula

A(n,k) = binomial(binomial(n + k - 1, n) + n - 1, n).