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A331436 Array read by antidiagonals: A(n,k) is the number of n element multisets of n element multisets of a k-set. 12
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 (list; table; graph; refs; listen; history; text; internal format)
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

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.

Sequence in context: A294042 A287316 A322280 * A210472 A320080 A246106

Adjacent sequences:  A331433 A331434 A331435 * A331437 A331438 A331439

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Jan 17 2020

STATUS

approved

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Last modified April 10 15:47 EDT 2021. Contains 342845 sequences. (Running on oeis4.)