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A330608 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.

%I A330608 #8 Feb 20 2020 13:58:02
%S A330608 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 A330608 110,72,26,6,1,14,35,185,366,306,135,37,7,1,0,70,460,1220,1300,702,
%U A330608 228,50,8,1,42,126,1150,4065,5525,3650,1406,357,65,9,1
%N A330608 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 A330608 Triangle starts:
%e A330608 [0] [ 1]
%e A330608 [1] [ 0,  1]
%e A330608 [2] [ 1,  1,   1]
%e A330608 [3] [ 0,  2,   2,    1]
%e A330608 [4] [ 2,  3,   5,    3,    1]
%e A330608 [5] [ 0,  6,  12,   10,    4,   1]
%e A330608 [6] [ 5, 10,  30,   33,   17,   5,   1]
%e A330608 [7] [ 0, 20,  74,  110,   72,  26,   6,  1]
%e A330608 [8] [14, 35, 185,  366,  306, 135,  37,  7, 1]
%e A330608 [9] [ 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1]
%p A330608 A053121 := (n, k, x) -> irem(n+k+1,2)*x^k*(k+1)*binomial(n+1,(n-k)/2)/(n+1):
%p A330608 P := (n, x) -> add(A053121(n, k, x), k=0..n):
%p A330608 seq(seq(P(n-k, k), k=0..n), n=0..10);
%Y A330608 Cf. A053121.
%K A330608 nonn,tabl
%O A330608 0,8
%A A330608 _Peter Luschny_, Jan 01 2020