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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
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
Sequence in context: A163910 A064777 A137784 * A347429 A211867 A003693
KEYWORD
nonn,nice
AUTHOR
Vladeta Jovovic, Mar 02 2000
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 11 2015
STATUS
approved

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