A307665 A(n,k) = Sum_{j=0..floor(n/k)} binomial(2*n,k*j+n), square array A(n,k) read by antidiagonals, for n >= 0, k >= 1.

1, 1, 3, 1, 2, 11, 1, 2, 7, 42, 1, 2, 6, 26, 163, 1, 2, 6, 21, 99, 638, 1, 2, 6, 20, 78, 382, 2510, 1, 2, 6, 20, 71, 297, 1486, 9908, 1, 2, 6, 20, 70, 262, 1145, 5812, 39203, 1, 2, 6, 20, 70, 253, 990, 4447, 22819, 155382, 1, 2, 6, 20, 70, 252, 936, 3796, 17358, 89846, 616666

Offset

0,3

Links

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

Example

Square array begins:
      1,    1,    1,    1,    1,    1,    1,    1, ...
      3,    2,    2,    2,    2,    2,    2,    2, ...
     11,    7,    6,    6,    6,    6,    6,    6, ...
     42,   26,   21,   20,   20,   20,   20,   20, ...
    163,   99,   78,   71,   70,   70,   70,   70, ...
    638,  382,  297,  262,  253,  252,  252,  252, ...
   2510, 1486, 1145,  990,  936,  925,  924,  924, ...
   9908, 5812, 4447, 3796, 3523, 3446, 3433, 3432, ...

Mathematica

T[n_, k_] := Sum[Binomial[2*n, k*j + n], {j, 0, Floor[n/k]}]; Table[T[n - k, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten (* Amiram Eldar, May 13 2021*)

Crossrefs

Columns 1-2 give A032443, A114121.

Cf. A306846, A306915, A307393, A307668.

Sequence in context: A301354 A229187 A126226 * A144156 A116854 A331692

Adjacent sequences: A307662 A307663 A307664 * A307666 A307667 A307668

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 20 2019

Status

approved