A383902 Square table read by ascending antidiagonals where T(n,k) = binomial(k+2^n-2,k).

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

Offset

0,8

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.

Links

Table of n, a(n) for n=0..65.

Example

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, ...

Maple

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

Crossrefs

Cf. A383905 (descending diagonals), A092056 (no restriction on totality)

Sequence in context: A264434 A151511 A048993 * A264431 A357941 A257050

Adjacent sequences: A383899 A383900 A383901 * A383903 A383904 A383905

Keyword

nonn,tabl

Author

Isaac R. Browne, May 15 2025

Status

approved