A307665 - OEIS

%I #15 May 13 2021 02:35:15

%S 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,

%T 2510,1,2,6,20,71,297,1486,9908,1,2,6,20,70,262,1145,5812,39203,1,2,6,

%U 20,70,253,990,4447,22819,155382,1,2,6,20,70,252,936,3796,17358,89846,616666

%N 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.

%e Square array begins:

%e       1,    1,    1,    1,    1,    1,    1,    1, ...

%e       3,    2,    2,    2,    2,    2,    2,    2, ...

%e      11,    7,    6,    6,    6,    6,    6,    6, ...

%e      42,   26,   21,   20,   20,   20,   20,   20, ...

%e     163,   99,   78,   71,   70,   70,   70,   70, ...

%e     638,  382,  297,  262,  253,  252,  252,  252, ...

%e    2510, 1486, 1145,  990,  936,  925,  924,  924, ...

%e    9908, 5812, 4447, 3796, 3523, 3446, 3433, 3432, ...

%t 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*)

%Y Columns 1-2 give A032443, A114121.

%Y Cf. A306846, A306915, A307393, A307668.

%K nonn,tabl

%O 0,3

%A _Seiichi Manyama_, Apr 20 2019