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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241982 Number of endofunctions on [2n] where the largest cycle length equals n. 3
 1, 3, 93, 8600, 1719060, 604727424, 331079253120, 260480095349760, 278592031202284800, 388855261570122547200, 686533182382689959116800, 1495779844806108697677004800, 3942052104672989614027181260800, 12360865524060039746012601384960000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..198 FORMULA a(n) = A241981(2n,n). a(n) ~ 2^(3*n+1/2) * n^(2*n-1) / exp(n). - Vaclav Kotesovec, Aug 19 2014 EXAMPLE a(1) = 3: (1,1), (1,2), (2,2). MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add((i-1)!^j*multinomial(n, n-i*j, i\$j)/j!*       b(n-i*j, i-1), j=0..n/i)))     end: A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, min(j, k)), j=0..n): a:= n-> `if`(n=0, 1, A(2*n, n) -A(2*n, n-1)): seq(a(n), n=0..15); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = Which[n==0, 1, i<1, 0, True, Sum[(i-1)!^j* multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], {j, 0, n/i} ] ]; A[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, Min[j, k]], {j, 0, n}]; a[n_] := If[n == 0, 1, A[2n, n] - A[2n, n-1]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 01 2017, translated from Maple *) CROSSREFS Cf. A241981, A246050. Sequence in context: A288070 A116292 A139543 * A037113 A142887 A297489 Adjacent sequences:  A241979 A241980 A241981 * A241983 A241984 A241985 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 10 2014 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 November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)