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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. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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 A292783

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

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Last modified May 29 10:41 EDT 2020. Contains 334699 sequences. (Running on oeis4.)