A308500 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=0..n} binomial(k*n,k*j).

1, 1, 2, 1, 2, 3, 1, 2, 4, 4, 1, 2, 8, 8, 5, 1, 2, 22, 32, 16, 6, 1, 2, 72, 170, 128, 32, 7, 1, 2, 254, 992, 1366, 512, 64, 8, 1, 2, 926, 6008, 16512, 10922, 2048, 128, 9, 1, 2, 3434, 37130, 215766, 261632, 87382, 8192, 256, 10, 1, 2, 12872, 232562, 2973350, 6643782, 4196352, 699050, 32768, 512, 11

Offset

0,3

Links

Seiichi Manyama, Antidiagonals n = 0..115, flattened

Example

Square array begins:
   1,  1,    1,     1,       1,         1, ...
   2,  2,    2,     2,       2,         2, ...
   3,  4,    8,    22,      72,       254, ...
   4,  8,   32,   170,     992,      6008, ...
   5, 16,  128,  1366,   16512,    215766, ...
   6, 32,  512, 10922,  261632,   6643782, ...
   7, 64, 2048, 87382, 4196352, 215492564, ...

Mathematica

T[n_, k_] := Sum[Binomial[k*n, k*j], {j, 0, n}] ; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 12 2021 *)

Crossrefs

Columns k=0..10 give A000027(n+1), A000079, A081294, A007613, A070775, A070782, A070967, A094211, A070832, A094213, A070833.

Main diagonal gives A167009.

Sequence in context: A347570 A116925 A309010 * A210950 A214314 A209435

Adjacent sequences: A308497 A308498 A308499 * A308501 A308502 A308503

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 01 2019

Status

approved