The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A211603 Triangular array read by rows: T(n,k) is the number of n-permutations that are pure cycles having exactly k fixed points; n>=2, 0<=k<=n-2. 4
 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, 3628800, 3991680, 2217600, 831600, 237600, 55440, 11088, 1980, 330, 55 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A006231 (row sums), A008290, A092271, A111492, A238363. Sequence in context: A284385 A282940 A193909 * A221956 A249549 A193905 Adjacent sequences:  A211600 A211601 A211602 * A211604 A211605 A211606 KEYWORD nonn,tabl,easy AUTHOR Geoffrey Critzer, Feb 10 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)