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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.

%I A306100 #37 Sep 28 2018 05:25:34
%S A306100 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,
%T A306100 6,55,228,525,378,48,0,1,7,78,430,1540,2334,1242,86,0,1,8,105,726,
%U A306100 3605,8964,11100,3690,160,0,1,9,136,1134,7278,25980,56292,47496,11266,282,0
%N 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.
%H A306100 Alois P. Heinz, <a href="/A306100/b306100.txt">Antidiagonals n = 0..50, flattened</a>
%H A306100 OEIS wiki, <a href="/wiki/Plane_partitions">Plane partitions</a>.
%H A306100 Wikipedia, <a href="https://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>.
%F A306100 T(n,k) = Sum_{j=0..n} A091298(n,j)*k^j, assuming A091298(n,0) = A000007(n).
%F A306100 T(n,k) = Sum_{i=0..k} C(k,i) * A319600(n,i). - _Alois P. Heinz_, Sep 28 2018
%e A306100 The array starts:
%e A306100   [1  1    1     1     1      1 ...] = A000012
%e A306100   [0  1    2     3     4      5 ...] = A001477
%e A306100   [0  3   10    21    36     55 ...] = A014105
%e A306100   [0  6   34   102   228    430 ...] = A067389
%e A306100   [0 13  122   525  1540   3605 ...]
%e A306100   [0 24  378  2334  8964  25980 ...]
%e A306100   [0 48 1242 11100 56292 203280 ...]
%o A306100 (PARI) A306100(n,k)=sum(j=1,n,A091298(n,j)*k^j)
%Y A306100 Columns k=0-5 give: A000007, A000219, A306099, A306093, A306094, A306095.
%Y A306100 See A306101 for a variant.
%Y A306100 Cf. A091298, A208447, A001477, A014105, A067389.
%K A306100 nonn,tabl
%O A306100 0,8
%A A306100 _M. F. Hasler_, Sep 22 2018
%E A306100 Edited by _Alois P. Heinz_, Sep 26 2018