cp's OEIS Frontend

A102709 Let a(n,m) = card{f^(n) : f is a mapping from a set of m elements into itself}, where f^(l)(x) = f^(l-1)(f(x)),l>0, f^(0)(x) = x; sequence gives a(n,5).

%I A102709 #13 Sep 08 2015 17:04:33
%S A102709 1,3125,1075,985,580,1281,295,1305,580,925,631,1305,220,1305,655,901,
%T A102709 580,1305,295,1305,556,925,655,1305,220,1281,655,925,580,1305,271,
%U A102709 1305,580,925,655,1281,220,1305,655,925,556,1305,295,1305,580,901,655,1305,220
%N A102709 Let a(n,m) = card{f^(n) : f is a mapping from a set of m elements into itself}, where f^(l)(x) = f^(l-1)(f(x)),l>0, f^(0)(x) = x; sequence gives a(n,5).
%C A102709 Sequence appears to have a rational o.g.f. - _Ralf Stephan_, May 18 2007
%H A102709 Ray Chandler, <a href="/A102709/b102709.txt">Table of n, a(n) for n = 0..10000</a>
%H A102709 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (-1, -2, -2, -2, -1, 0, 1, 2, 2, 2, 1, 1).
%F A102709 Empirical g.f.: 1+x*(60*x^14 +480*x^13 +2360*x^12 +2584*x^11 +3099*x^10 +2188*x^9 -522*x^8 -4057*x^7 -8367*x^6 -9981*x^5 -12231*x^4 -9965*x^3 -8310*x^2 -4200*x -3125) / ((x -1)*(x +1)*(x^2 -x +1)*(x^2 +1)*(x^2 +x +1)*(x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Aug 07 2013
%t A102709 Join[{1, 3125, 1075, 985},LinearRecurrence[{-1, -2, -2, -2, -1, 0, 1, 2, 2, 2, 1, 1},{580, 1281, 295, 1305, 580, 925, 631, 1305, 220, 1305, 655, 901},45]] (* _Ray Chandler_, Sep 08 2015 *)
%Y A102709 Cf. A102687.
%Y A102709 Row n=5 of A247026.
%K A102709 nonn
%O A102709 0,2
%A A102709 _Vladeta Jovovic_, Feb 05 2005
%E A102709 a(0) inserted by _Alois P. Heinz_, Sep 10 2014