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