A306100 Square array T(n,k) = number of plane partitions of n with parts colored in (at most) k colors; n >= 0, k >= 0; read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 10, 6, 0, 1, 4, 21, 34, 13, 0, 1, 5, 36, 102, 122, 24, 0, 1, 6, 55, 228, 525, 378, 48, 0, 1, 7, 78, 430, 1540, 2334, 1242, 86, 0, 1, 8, 105, 726, 3605, 8964, 11100, 3690, 160, 0, 1, 9, 136, 1134, 7278, 25980, 56292, 47496, 11266, 282, 0

Offset

0,8

Links

Alois P. Heinz, Antidiagonals n = 0..50, flattened

OEIS wiki, Plane partitions.

Wikipedia, Plane partition.

Formula

T(n,k) = Sum_{j=0..n} A091298(n,j)*k^j, assuming A091298(n,0) = A000007(n).

T(n,k) = Sum_{i=0..k} C(k,i) * A319600(n,i). - Alois P. Heinz, Sep 28 2018

Example

The array starts:
  [1  1    1     1     1      1 ...] = A000012
  [0  1    2     3     4      5 ...] = A001477
  [0  3   10    21    36     55 ...] = A014105
  [0  6   34   102   228    430 ...] = A067389
  [0 13  122   525  1540   3605 ...]
  [0 24  378  2334  8964  25980 ...]
  [0 48 1242 11100 56292 203280 ...]

Prog

(PARI) A306100(n, k)=sum(j=1, n, A091298(n, j)*k^j)

Crossrefs

Columns k=0-5 give: A000007, A000219, A306099, A306093, A306094, A306095.

See A306101 for a variant.

Cf. A091298, A208447, A001477, A014105, A067389.

Sequence in context: A307910 A128888 A305401 * A294046 A320079 A349971

Adjacent sequences: A306097 A306098 A306099 * A306101 A306102 A306103

Keyword

nonn,tabl

Author

M. F. Hasler, Sep 22 2018

Extensions

Edited by Alois P. Heinz, Sep 26 2018

Status

approved