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%I #16 Sep 28 2018 11:37:02
%S 1,0,1,0,3,4,0,6,22,18,0,13,96,198,120,0,24,330,1272,1800,840,0,48,
%T 1146,7518,19152,20640,7920,0,86,3518,36684,148200,274080,234720,
%U 75600,0,160,10946,177438,1080960,3083640,4462560,3180240,887040,0,282,32102,788928,6952440,28621920,62056080,73175760,44432640,10886400
%N Number T(n,k) of plane partitions of n into parts of exactly k sorts; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%H Alois P. Heinz, <a href="/A319600/b319600.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) = Sum_{i=0..k} (-1)^i * C(k,i) * A306100(n,k-i).
%F T(n,k) = k! * A319730(n,k).
%e Triangle T(n,k) begins:
%e 1;
%e 0, 1;
%e 0, 3, 4;
%e 0, 6, 22, 18;
%e 0, 13, 96, 198, 120;
%e 0, 24, 330, 1272, 1800, 840;
%e 0, 48, 1146, 7518, 19152, 20640, 7920;
%e 0, 86, 3518, 36684, 148200, 274080, 234720, 75600;
%e 0, 160, 10946, 177438, 1080960, 3083640, 4462560, 3180240, 887040;
%Y Columns k=0-1 give: A000007, A000219 (for n>0).
%Y Row sums give A319601.
%Y Main diagonal gives A053529.
%Y Cf. A255970, A319730.
%K nonn,tabl
%O 0,5
%A _Alois P. Heinz_, Sep 24 2018
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