A383905 Square table read by descending antidiagonals where T(n,k) = binomial(k+2^n-2,k).

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 7, 1, 0, 1, 10, 28, 15, 1, 0, 1, 15, 84, 120, 31, 1, 0, 1, 21, 210, 680, 496, 63, 1, 0, 1, 28, 462, 3060, 5456, 2016, 127, 1, 0, 1, 36, 924, 11628, 46376, 43680, 8128, 255, 1, 0, 1, 45, 1716, 38760, 324632, 720720, 349504, 32640, 511, 1

Offset: 0

Author

Isaac R. Browne, May 15 2025

Keywords

• nonn
• tabl

Comments

T(n,k) is the number of right total relations between a set of n distinguishable elements and a set of k indistinguishable elements.

Examples

			Rows start:
    1,  0,   0,   0,    0, ...
    1,  1,   1,   1,    1, ...
    1,  3,   6,  10,   15, ...
    1,  7,  28,  84,  210, ...
    1, 15, 120, 680, 3060, ...
		

Crossrefs

Cf. A383902 (ascending diagonals), A137153 (no restriction on totality).

Programs

Maple

T:= (n, k)-> binomial(k+2^n-2, k):
seq(seq(T(n, d-n), n=0..d), d=0..10);  # Alois P. Heinz, May 16 2025