%I #24 Sep 12 2020 02:23:16

%S 0,0,1,0,1,2,0,1,4,3,0,1,10,23,4,0,1,28,259,176,5,0,1,82,3527,12916,

%T 1689,6,0,1,244,51331,1213136,1057221,19524,7,0,1,730,762743,

%U 123296356,885533769,128816766,264207,8,0,1,2188,11406979,12820180976,809068942341,1179489355164,21878089479,4098240,9

%N Square array T(n,k), n>=0, k>=0, read by antidiagonals: T(n,k) = ((2n-1)!!)^k * Sum_{i=1..n} 1/(2*i-1)^k.

%H Seiichi Manyama, <a href="/A291656/b291656.txt">Antidiagonals n = 0..54, flattened</a>

%F T(0,k) = 0, T(1,k) = 1 and T(n+1, k) = ((2*n-1)^k+(2*n+1)^k) * T(n, k) - (2*n-1)^(2*k) * T(n-1, k).

%e Square array begins:

%e 0, 0, 0, 0, 0, ...

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

%e 2, 4, 10, 28, 82, ...

%e 3, 23, 259, 3527, 51331, ...

%e 4, 176, 12916, 1213136, 123296356, ...

%Y Columns k=0-5 give: A001477, A004041(n+1), A001824(n+1), A291585, A291586, A291587.

%Y Rows n=0-2 give: A000004, A000012, A034472.

%Y Main diagonal gives A291676.

%Y Cf. A291556.

%K nonn,tabl

%O 0,6

%A _Seiichi Manyama_, Aug 28 2017