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A306101 Square array T(n,k) = number of plane partitions of n with parts colored in (at most) k colors; n, k >= 1; read by antidiagonals. 7
1, 2, 3, 3, 10, 6, 4, 21, 34, 13, 5, 36, 102, 122, 24, 6, 55, 228, 525, 378, 48, 7, 78, 430, 1540, 2334, 1242, 86, 8, 105, 726, 3605, 8964, 11100, 3690, 160, 9, 136, 1134, 7278, 25980, 56292, 47496, 11266, 282, 10, 171, 1672, 13237, 62574, 203280, 316388, 210756, 32666, 500, 11, 210, 2358, 22280, 132258, 586878, 1417530 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

One could have included a row 0 with all 1's, since there is exactly one partition of n = 0, the empty sum, for which all terms (since there are none) are colored in one among k colors.

LINKS

Alois P. Heinz, Antidiagonals n = 1..50, flattened

FORMULA

T(n,k) = Sum_{j=1..n} A091298(n,j)*k^j.

EXAMPLE

The array starts:

  [      1       2       3       4       5 ...] = A000027

  [      3      10      21      36      55 ...] = A014105

  [      6      34     102     228     430 ...] = A067389

  [     13     122     525    1540    3605 ...]

  [     24     378    2334    8964   25980 ...]

  [     48    1242   11100   56292  203280 ...]

   A000219 A306099 A306093 A306094 A306094

For concrete examples, see A306099 and A306093.

PROG

(PARI) A306101(n, k)=sum(j=1, n, A091298(n, j)*k^j)

CROSSREFS

Cf. A091298, A208447, A000219, A000027, A014105, A067389.

See A306100 for a variant.

Cf. A000219, A306099, A306093, A306094, A306095 for columns 1..5.

Sequence in context: A340914 A194232 A110042 * A337432 A123027 A100652

Adjacent sequences:  A306098 A306099 A306100 * A306102 A306103 A306104

KEYWORD

nonn,tabl

AUTHOR

M. F. Hasler, Sep 22 2018

STATUS

approved

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Last modified May 13 12:02 EDT 2021. Contains 343839 sequences. (Running on oeis4.)