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%I #15 Jan 31 2020 15:36:16
%S 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,
%T 120,1540,3060,252,1,0,1,7,231,7770,73815,53130,924,1,0,1,8,406,30856,
%U 1088430,5461512,1107568,3432,1,0,1,9,666,102340,11009376,286243776,581106988,26978328,12870,1,0
%N Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set.
%H Andrew Howroyd, <a href="/A331436/b331436.txt">Table of n, a(n) for n = 0..1325</a>
%F A(n,k) = binomial(binomial(n + k - 1, n) + n - 1, n).
%e Array begins:
%e ==================================================================
%e n\k | 0 1 2 3 4 5 6
%e ----+-------------------------------------------------------------
%e 0 | 1 1 1 1 1 1 1 ...
%e 1 | 0 1 2 3 4 5 6 ...
%e 2 | 0 1 6 21 55 120 231 ...
%e 3 | 0 1 20 220 1540 7770 30856 ...
%e 4 | 0 1 70 3060 73815 1088430 11009376 ...
%e 5 | 0 1 252 53130 5461512 286243776 8809549056 ...
%e 6 | 0 1 924 1107568 581106988 127860662755 13949678575756 ...
%e ...
%e The A(2,2) = 6 multisets are:
%e {{1,1}, {1,1}},
%e {{1,1}, {1,2}},
%e {{1,1}, {2,2}},
%e {{1,2}, {1,2}},
%e {{1,2}, {2,2}},
%e {{2,2}, {2,2}}.
%o (PARI) T(n,k)={binomial(binomial(n + k - 1, n) + n - 1, n)}
%o { for(n=0, 7, for(k=0, 7, print1(T(n,k), ", ")); print) }
%Y Rows n=0..3 are A000012, A001477, A002817, A140236.
%Y Columns k=0..10 are A000007, A000012, A000984, A099121, A099122, A099123, A099124, A099125, A099126, A099127, A099128.
%Y Min diagonal is A331477.
%K nonn,tabl
%O 0,8
%A _Andrew Howroyd_, Jan 17 2020
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