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A331436
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Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set.
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12
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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
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OFFSET
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0,8
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LINKS
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FORMULA
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A(n,k) = binomial(binomial(n + k - 1, n) + n - 1, n).
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EXAMPLE
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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}}.
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PROG
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(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) }
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CROSSREFS
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Columns k=0..10 are A000007, A000012, A000984, A099121, A099122, A099123, A099124, A099125, A099126, A099127, A099128.
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KEYWORD
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AUTHOR
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STATUS
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approved
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