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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).
0
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
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jul 05 2014
STATUS
approved