login
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
OFFSET
0,8
LINKS
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.
Sequence in context: A307910 A128888 A305401 * A294046 A320079 A349971
KEYWORD
nonn,tabl
AUTHOR
M. F. Hasler, Sep 22 2018
EXTENSIONS
Edited by Alois P. Heinz, Sep 26 2018
STATUS
approved