%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