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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.)