A331477 Number of n element multisets of n element multisets of an n-set.

1, 1, 6, 220, 73815, 286243776, 13949678575756, 8800321588119330984, 73241437035618231162682185, 8183604949527627465377060678018870, 12477686558866630120430437118910496237274716, 263383624455446425760290611316122951917033704595478840

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..40

Formula

a(n) = binomial(binomial(2*n - 1, n) + n - 1, n).

Example

The a(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}}.

Mathematica

Table[Binomial[Binomial[2n-1, n]+n-1, n], {n, 0, 20}] (* Harvey P. Dale, Aug 19 2021 *)

Prog

(PARI) a(n)={binomial(binomial(2*n - 1, n) + n - 1, n)}

Crossrefs

Main diagonal of A331436.

Sequence in context: A041623 A292692 A015477 * A144658 A203637 A144045

Adjacent sequences: A331474 A331475 A331476 * A331478 A331479 A331480

Keyword

nonn

Author

Andrew Howroyd, Jan 17 2020

Status

approved