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

0,3

Links

Table of n, a(n) for n=0..44.

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

Example

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;
  ...

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 *)

Crossrefs

This is A099174 without the two rightmost diagonals.

Sequence in context: A193451 A335809 A322215 * A210838 A319256 A354618

Adjacent sequences: A244489 A244490 A244491 * A244493 A244494 A244495

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 05 2014

Status

approved