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%I #17 Sep 28 2018 11:37:10
%S 1,0,1,0,3,2,0,6,11,3,0,13,48,33,5,0,24,165,212,75,7,0,48,573,1253,
%T 798,172,11,0,86,1759,6114,6175,2284,326,15,0,160,5473,29573,45040,
%U 25697,6198,631,22,0,282,16051,131488,289685,238516,86189,14519,1102,30
%N Number T(n,k) of plane partitions of n into parts of exactly k sorts which are introduced in ascending order; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%H Alois P. Heinz, <a href="/A319730/b319730.txt">Rows n = 0..50, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlanePartition.html">Plane partition</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>
%F T(n,k) = 1/k! * A319600(n,k).
%e Triangle T(n,k) begins:
%e 1;
%e 0, 1;
%e 0, 3, 2;
%e 0, 6, 11, 3;
%e 0, 13, 48, 33, 5;
%e 0, 24, 165, 212, 75, 7;
%e 0, 48, 573, 1253, 798, 172, 11;
%e 0, 86, 1759, 6114, 6175, 2284, 326, 15;
%e 0, 160, 5473, 29573, 45040, 25697, 6198, 631, 22;
%e 0, 282, 16051, 131488, 289685, 238516, 86189, 14519, 1102, 30;
%Y Columns k=0-1 give: A000007, A000219 (for n>0).
%Y Main diagonal gives A000041.
%Y Row sums give A319731.
%Y T(2n,n) gives A319732.
%Y Cf. A256130, A319600.
%K nonn,tabl
%O 0,5
%A _Alois P. Heinz_, Sep 26 2018
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