The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A053195 Number of level permutations of degree n. 3
 1, 1, 2, 3, 18, 45, 360, 1575, 20790, 99225, 1332450, 9823275, 181496700, 1404728325, 26221595400, 273922023375, 7196040101250, 69850115960625, 1662139682453250, 22561587455281875, 675158520854317500, 9002073394657468125, 259715927440434465000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A permutation is level if the powers of 2 dividing its cycle lengths are all equal. For odd n, level permutations of degree n are just permutations that have odd order, i.e., A053195(2*n+1) = A000246(2*n+1). - Vladeta Jovovic, Sep 29 2004 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 L. Babai and P. J. Cameron, Automorphisms and enumeration of switching classes of tournaments, Electron. J. Combin., 7 (2000), no. 1, Research Paper 38, 25 pp. MAPLE with(combinat): b:= proc(n, i, p) option remember; `if`(n=0, 1, `if`(i<1, 0, add(multinomial(n, n-i*j, i\$j)/j!*(i-1)!^j* b(n-i*j, i-2*p, p), j=0..n/i))) end: a:= n-> (m-> `if`(n=0, 1, add(b(n, (h-> h-1+irem(h, 2) )(iquo(n, 2^j))*2^j, 2^j), j=0..m)))(ilog2(n)): seq(a(n), n=0..25); # Alois P. Heinz, Jun 11 2015 MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, p_] := b[n, i, p] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*(i-1)!^j*b[n - i*j, i-2*p, p], {j, 0, n/i}]]]; a[n_] := Function[{m}, If[n == 0, 1, Sum[ b[n, Function [{h}, h - 1 + Mod[h, 2]][Quotient[n, 2^j]]*2^j, 2^j], {j, 0, m}]]][Log[2, n] // Floor]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jul 07 2015, after Alois P. Heinz *) CROSSREFS Cf. A049313, A053197. Sequence in context: A163910 A064777 A137784 * A347429 A211867 A003693 Adjacent sequences: A053192 A053193 A053194 * A053196 A053197 A053198 KEYWORD nonn,nice AUTHOR Vladeta Jovovic, Mar 02 2000 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Jun 11 2015 STATUS approved

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

Last modified May 18 15:04 EDT 2024. Contains 372641 sequences. (Running on oeis4.)