OFFSET
2,2
COMMENTS
Equivalently, T(n,k) is the number of n-permutations that are pure cycles of length n-k.
Row sums = A006231.
With a different row and column indexing, this triangle equals the infinitesimal generator of A008290. Equals the unsigned version of A238363, omitting its main diagonal. See also A092271. - Peter Bala, Feb 13 2017
LINKS
Alois P. Heinz, Rows n = 2..150, flattened
FORMULA
E.g.f.: exp(y*x)*(log(1/(1-x))-x).
T(n,k) = C(n,k)*(n-k-1)!. - Alois P. Heinz, Feb 10 2013
T(n,k) = A111492(n,n-k). - R. J. Mathar, Mar 07 2013
EXAMPLE
T(3,1) = 3 because we have (1)(2,3), (2)(1,3), (3)(1,2).
1;
2, 3;
6, 8, 6;
24, 30, 20, 10;
120, 144, 90, 40, 15;
720, 840, 504, 210, 70, 21;
5040, 5760, 3360, 1344, 420, 112, 28;
40320, 45360, 25920, 10080, 3024, 756, 168, 36;
362880, 403200, 226800, 86400, 25200, 6048, 1260, 240, 45;
MAPLE
T:= (n, k)-> binomial(n, k)*(n-k-1)!:
seq(seq(T(n, k), k=0..n-2), n=2..12); # Alois P. Heinz, Feb 10 2013
MATHEMATICA
nn=10; f[list_]:=Select[list, #>0&]; Map[f, Range[0, nn]!CoefficientList[ Series[Exp[y x](Log[1/(1-x)]-x), {x, 0, nn}], {x, y}]]//Grid
CROSSREFS
KEYWORD
AUTHOR
Geoffrey Critzer, Feb 10 2013
STATUS
approved