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%I #14 Mar 01 2023 04:46:01
%S 1,3,15,84,660,4680,47880,463680,5261760,59875200,858211200,
%T 11256537600,183697113600,2833294464000,47730114432000,
%U 847372990464000,17250840262656000,329722245844992000,7359528574734336000,156922179527393280000,3601911423105515520000,84862054947209379840000
%N n! times sum of Farey fractions of order n.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FareySequence.html">Farey Sequence</a>.
%e Multiplication of n-th-order positive Farey fractions by n! gives the integer sequence A002088(n), for n>=1. Arrange them in rows:
%e 1
%e 1 2
%e 2 3 4 6
%e 6 8 12 16 18 24
%e The sum over row 4 is a(4)=84.
%t Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[n!Plus @@ Farey[n], {n, 0, 20}] (* _Robert G. Wilson v_, Apr 06 2004 *)
%o (PARI) a(n) = my(list = List()); for (k=1, n, for (m=1, k, listput(list, m/k); ); ); n!*vecsum(Set(Vec(list))); \\ _Michel Marcus_, Mar 01 2023
%Y Cf. A002088, A092824, A093594.
%K nonn
%O 1,2
%A _Clark Kimberling_, Apr 03 2004
%E More terms from _Robert G. Wilson v_, Apr 06 2004
%E More terms from _Michel Marcus_, Mar 01 2023
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