A360604 Triangle read by rows. T(n, k) = 2^binomial(n - k, 2) * binomial(n - 1, k - 1).

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 8, 6, 3, 1, 0, 64, 32, 12, 4, 1, 0, 1024, 320, 80, 20, 5, 1, 0, 32768, 6144, 960, 160, 30, 6, 1, 0, 2097152, 229376, 21504, 2240, 280, 42, 7, 1, 0, 268435456, 16777216, 917504, 57344, 4480, 448, 56, 8, 1

Offset: 0

Author

Peter Luschny, Feb 23 2023

Keywords

• nonn
• tabl

Examples

			Triangle T(n, k) starts:
[0] 1;
[1] 0,       1;
[2] 0,       1,      1;
[3] 0,       2,      2,     1;
[4] 0,       8,      6,     3,    1;
[5] 0,      64,     32,    12,    4,   1;
[6] 0,    1024,    320,    80,   20,   5,  1;
[7] 0,   32768,   6144,   960,  160,  30,  6, 1;
[8] 0, 2097152, 229376, 21504, 2240, 280, 42, 7, 1;
		

Crossrefs

Cf. A006125 (column 1), A002378 (T(n+2,n)), A130809 (T(n+3,n)), A006896 (row sums).

Programs

Maple

T := (n, k) -> 2^binomial(n - k, 2) * binomial(n-1, k-1):
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;