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

1,7

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A052799 A229569 A179964 * A029574 A119540 A052784

Adjacent sequences: A153757 A153758 A153759 * A153761 A153762 A153763

Keyword

nonn

Author

Franz Vrabec, Jan 01 2009

Extensions

More terms from Alois P. Heinz, Feb 16 2013

Status

approved