%I #17 Mar 18 2023 08:07:45

%S 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,

%T 253,598,351,7,1,1,8,73,506,2073,3601,1275,8,1,1,9,99,889,5351,17577,

%U 22165,4707,9,1,1,10,129,1429,11515,58481,152173,138445,17577,10,1

%N 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).

%H Seiichi Manyama, <a href="/A358146/b358146.txt">Antidiagonals n = 0..139, flattened</a>

%e Square array begins:

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

%e 1, 2, 3, 4, 5, 6, ...

%e 1, 3, 9, 19, 33, 51, ...

%e 1, 4, 29, 103, 253, 506, ...

%e 1, 5, 99, 598, 2073, 5351, ...

%e 1, 6, 351, 3601, 17577, 58481, ...

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

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

%Y Main diagonal gives A226391.

%Y Cf. A358050.

%K nonn,tabl

%O 0,5

%A _Seiichi Manyama_, Oct 31 2022