A291656 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.

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, 1689, 6, 0, 1, 244, 51331, 1213136, 1057221, 19524, 7, 0, 1, 730, 762743, 123296356, 885533769, 128816766, 264207, 8, 0, 1, 2188, 11406979, 12820180976, 809068942341, 1179489355164, 21878089479, 4098240, 9

Offset

0,6

Links

Seiichi Manyama, Antidiagonals n = 0..54, flattened

Formula

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).

Example

Square array begins:
  0,   0,     0,       0,         0, ...
  1,   1,     1,       1,         1, ...
  2,   4,    10,      28,        82, ...
  3,  23,   259,    3527,     51331, ...
  4, 176, 12916, 1213136, 123296356, ...

Crossrefs

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

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

Main diagonal gives A291676.

Cf. A291556.

Sequence in context: A342133 A358050 A334781 * A209063 A342321 A098689

Adjacent sequences: A291653 A291654 A291655 * A291657 A291658 A291659

Keyword

nonn,tabl

Author

Seiichi Manyama, Aug 28 2017

Status

approved