A393312 Triangle read by rows: T(n,k) = (n-k-1)! * binomial(n,k) if n+k is odd, else 0.

0, 1, 0, 0, 2, 0, 2, 0, 3, 0, 0, 8, 0, 4, 0, 24, 0, 20, 0, 5, 0, 0, 144, 0, 40, 0, 6, 0, 720, 0, 504, 0, 70, 0, 7, 0, 0, 5760, 0, 1344, 0, 112, 0, 8, 0, 40320, 0, 25920, 0, 3024, 0, 168, 0, 9, 0, 0, 403200, 0, 86400, 0, 6048, 0, 240, 0, 10, 0

Offset

0,5

Comments

Non-standard exponential Riordan array (arctanh(x), x).

Links

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

Formula

T(n,k) = (n-k-1)! * binomial(n,k) if n+k is odd, else 0.

E.g.f. for column k: x^k/k!*arctanh(x).

Example

Triangle begins:
  0;
  1,  0;
  0,  2,  0;
  2,  0,  3,  0;
  0,  8,  0,  4,  0;
 24,  0, 20,  0,  5,  0;
  0,144,  0, 40,  0,  6,  0;
...

Crossrefs

Row sums give A291484.

Cf. A005359, A007318.

Sequence in context: A239246 A171700 A162660 * A324848 A090330 A332447

Adjacent sequences: A393309 A393310 A393311 * A393313 A393314 A393315

Keyword

nonn,tabl

Author

Zhuorui He, Feb 10 2026

Status

approved