A153760 Number of degree-n permutations of order exactly 7.

0, 0, 0, 0, 0, 0, 720, 5760, 25920, 86400, 237600, 570240, 1235520, 892045440, 13348249200, 106757164800, 604924594560, 2722120577280, 10344007402560, 34479959558400, 24928970490633600, 546446134633639680, 6281586217487489040, 50248618811434961280

Offset: 1

Author

Franz Vrabec, Jan 01 2009

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200

Crossrefs

Column k=7 of A057731. - Alois P. Heinz, Feb 16 2013

Programs

Maple

a:= proc(n) option remember;
      `if`(n<7, 0, a(n-1)+(1+a(n-7))*(n-1)!/(n-7)!)
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Feb 16 2013

Mathematica

Rest[CoefficientList[Series[-Exp[x] + Exp[x + 1/7*x^7], {x, 0, 25}], x]*Range[0, 25]!] (* G. C. Greubel, Aug 27 2016 *)

PARI

seq(n)={Vec(serlaplace(-exp(x + O(x*x^n)) + exp(x + x^7/7 + O(x*x^n))),-n)} \\ Andrew Howroyd, Jul 02 2018

Formula

E.g.f.: -exp(x)+exp(x+1/7*x^7). - Alois P. Heinz, Feb 16 2013

Extensions

More terms from Alois P. Heinz, Feb 16 2013