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%I #8 Feb 20 2020 13:58:02
%S 1,0,1,1,1,1,0,2,2,1,2,3,5,3,1,0,6,12,10,4,1,5,10,30,33,7,5,1,0,20,74,
%T 110,72,26,6,1,14,35,185,366,306,135,37,7,1,0,70,460,1220,1300,702,
%U 228,50,8,1,42,126,1150,4065,5525,3650,1406,357,65,9,1
%N T(n, k) = P(n-k, k) where P(n, x) = Sum_{k=0..n} A053121(n, k)*x^k. Triangle read by rows, for 0 <= k <= n.
%e Triangle starts:
%e [0] [ 1]
%e [1] [ 0, 1]
%e [2] [ 1, 1, 1]
%e [3] [ 0, 2, 2, 1]
%e [4] [ 2, 3, 5, 3, 1]
%e [5] [ 0, 6, 12, 10, 4, 1]
%e [6] [ 5, 10, 30, 33, 17, 5, 1]
%e [7] [ 0, 20, 74, 110, 72, 26, 6, 1]
%e [8] [14, 35, 185, 366, 306, 135, 37, 7, 1]
%e [9] [ 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1]
%p A053121 := (n, k, x) -> irem(n+k+1,2)*x^k*(k+1)*binomial(n+1,(n-k)/2)/(n+1):
%p P := (n, x) -> add(A053121(n, k, x), k=0..n):
%p seq(seq(P(n-k, k), k=0..n), n=0..10);
%Y Cf. A053121.
%K nonn,tabl
%O 0,8
%A _Peter Luschny_, Jan 01 2020
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