A358146 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 9, 4, 1, 1, 5, 19, 29, 5, 1, 1, 6, 33, 103, 99, 6, 1, 1, 7, 51, 253, 598, 351, 7, 1, 1, 8, 73, 506, 2073, 3601, 1275, 8, 1, 1, 9, 99, 889, 5351, 17577, 22165, 4707, 9, 1, 1, 10, 129, 1429, 11515, 58481, 152173, 138445, 17577, 10, 1

Offset

0,5

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Example

Square array begins:
  1, 1,   1,    1,     1,     1, ...
  1, 2,   3,    4,     5,     6, ...
  1, 3,   9,   19,    33,    51, ...
  1, 4,  29,  103,   253,   506, ...
  1, 5,  99,  598,  2073,  5351, ...
  1, 6, 351, 3601, 17577, 58481, ...

Prog

(PARI) T(n, k) = sum(j=0, n, binomial(k*j, j));

Crossrefs

Columns k=0-5 give: A000012, A001477(n+1), A006134, A188675, A225612, A225615.

Main diagonal gives A226391.

Cf. A358050.

Sequence in context: A295205 A297020 A099597 * A283113 A123610 A209631

Adjacent sequences: A358143 A358144 A358145 * A358147 A358148 A358149

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 31 2022

Status

approved