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.

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, 110, 72, 26, 6, 1, 14, 35, 185, 366, 306, 135, 37, 7, 1, 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1, 42, 126, 1150, 4065, 5525, 3650, 1406, 357, 65, 9, 1

Offset: 0

Author

Peter Luschny, Jan 01 2020

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] [ 1]
[1] [ 0,  1]
[2] [ 1,  1,   1]
[3] [ 0,  2,   2,    1]
[4] [ 2,  3,   5,    3,    1]
[5] [ 0,  6,  12,   10,    4,   1]
[6] [ 5, 10,  30,   33,   17,   5,   1]
[7] [ 0, 20,  74,  110,   72,  26,   6,  1]
[8] [14, 35, 185,  366,  306, 135,  37,  7, 1]
[9] [ 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1]
		

Crossrefs

Cf. A053121.

Programs

Maple

A053121 := (n, k, x) -> irem(n+k+1,2)*x^k*(k+1)*binomial(n+1,(n-k)/2)/(n+1):
P := (n, x) -> add(A053121(n, k, x), k=0..n):
seq(seq(P(n-k, k), k=0..n), n=0..10);