A244492 Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = n!/(2^i*i!*k!), where k=n-2i (or 0 for entries with wrong parity).

1, 0, 3, 3, 0, 6, 0, 15, 0, 10, 15, 0, 45, 0, 15, 0, 105, 0, 105, 0, 21, 105, 0, 420, 0, 210, 0, 28, 0, 945, 0, 1260, 0, 378, 0, 36, 945, 0, 4725, 0, 3150, 0, 630, 0, 45

Offset: 0

Author

N. J. A. Sloane, Jul 05 2014

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    0,   3;
    3,   0,    6;
    0,  15,    0,   10;
   15,   0,   45,    0,   15;
    0, 105,    0,  105,    0,  21;
  105,   0,  420,    0,  210,   0,  28;
    0, 945,    0, 1260,    0, 378,   0, 36;
  945,   0, 4725,    0, 3150,   0, 630,  0, 45;
  ...
		

Links

• J. East and R. D. Gray, Idempotent generators in finite partition monoids and related semigroups, arXiv preprint arXiv:1404.2359 [math.GR], 2014-2016.

Crossrefs

This is A099174 without the two rightmost diagonals.

Programs

Mathematica

T[n_, k_] := With[{i = (n-k)/2}, If[EvenQ[n-k], n!/(2^i i! k!), 0]];
Table[T[n, k], {n, 2, 10}, {k, 0, n-2}] // Flatten (* Jean-François Alcover, Nov 25 2018 *)