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

%I A153760 #17 Jul 02 2018 22:38:07
%S A153760 0,0,0,0,0,0,720,5760,25920,86400,237600,570240,1235520,892045440,
%T A153760 13348249200,106757164800,604924594560,2722120577280,10344007402560,
%U A153760 34479959558400,24928970490633600,546446134633639680,6281586217487489040,50248618811434961280
%N A153760 Number of degree-n permutations of order exactly 7.
%H A153760 Alois P. Heinz, <a href="/A153760/b153760.txt">Table of n, a(n) for n = 1..200</a>
%F A153760 E.g.f.: -exp(x)+exp(x+1/7*x^7). - _Alois P. Heinz_, Feb 16 2013
%p A153760 a:= proc(n) option remember;
%p A153760       `if`(n<7, 0, a(n-1)+(1+a(n-7))*(n-1)!/(n-7)!)
%p A153760     end:
%p A153760 seq(a(n), n=1..30);  # _Alois P. Heinz_, Feb 16 2013
%t A153760 Rest[CoefficientList[Series[-Exp[x] + Exp[x + 1/7*x^7], {x, 0, 25}], x]*Range[0, 25]!] (* _G. C. Greubel_, Aug 27 2016 *)
%o A153760 (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
%Y A153760 Column k=7 of A057731. - _Alois P. Heinz_, Feb 16 2013
%K A153760 nonn
%O A153760 1,7
%A A153760 _Franz Vrabec_, Jan 01 2009
%E A153760 More terms from _Alois P. Heinz_, Feb 16 2013