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T(n, k) = P(n-k, k) where P(n, x) = Sum_{k=0..n} A064189(n, k)*x^k. Triangle read by rows, for 0 <= k <= n.
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%I #8 Feb 20 2020 13:57:17

%S 1,1,1,2,2,1,4,5,3,1,9,13,10,4,1,21,35,34,17,5,1,51,96,117,73,26,6,1,

%T 127,267,405,315,136,37,7,1,323,750,1407,1362,713,229,50,8,1,835,2123,

%U 4899,5895,3741,1419,358,65,9,1,2188,6046,17083,25528,19635,8796,2565,529,82,10,1

%N T(n, k) = P(n-k, k) where P(n, x) = Sum_{k=0..n} A064189(n, k)*x^k. Triangle read by rows, for 0 <= k <= n.

%e Triangle starts:

%e [0] 1

%e [1] 1, 1

%e [2] 2, 2, 1

%e [3] 4, 5, 3, 1

%e [4] 9, 13, 10, 4, 1

%e [5] 21, 35, 34, 17, 5, 1

%e [6] 51, 96, 117, 73, 26, 6, 1

%e [7] 127, 267, 405, 315, 136, 37, 7, 1

%e [8] 323, 750, 1407, 1362, 713, 229, 50, 8, 1

%e [9] 835, 2123, 4899, 5895, 3741, 1419, 358, 65, 9, 1

%p P := (n, x) -> add(A064189(n, k)*x^k, k=0..n):

%p seq(seq(P(n-k, k), k=0..n), n=0..10);

%Y Cf. A064189.

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Jan 01 2020