%I #32 Sep 08 2022 08:45:02
%S 0,2,24,182,1200,7502,45864,277622,1672800,10057502,60406104,
%T 362617862,2176246800,13059091502,78359364744,470170602902,
%U 2821066795200,16926530173502,101559568985784,609358577224742,3656154952230000
%N Jordan function J_n(6) (see A059379).
%C a(n) = A000225(n) * A024023(n) = (2^n - 1) * (3^n - 1) . a(n) is the number of n-tuples of elements e_1,e_2,...,e_n in the cyclic group C_6 such that the subgroup generated by e_1,e_2,...,e_n is C_6. - Sharon Sela (sharonsela(AT)hotmail.com), Jun 02 2002
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%H Vincenzo Librandi, <a href="/A059387/b059387.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).
%F G.f.: -2*x*(6*x^2-1) / ((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Dec 06 2012
%F a(n-1) = (limit of (Sum_{k>=0} (1/(6*k + 1)^s - 1/(6*k + 2)^s - 2/(6*k + 3)^s - 1/(6*k + 4)^s + 1/(6*k + 5)^s + 2/(6*k + 6)^s) as s -> n))/zeta(n)*6^(n - 1). - _Mats Granvik_, Nov 14 2013
%F a(n) = 2*A160869(n). - _R. J. Mathar_, Nov 23 2018
%p A059387:=n->(2^n-1)*(3^n-1); seq(A059387(n), n=0..50); # _Wesley Ivan Hurt_, Nov 14 2013
%t Table[(2^n-1)*(3^n-1),{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 28 2010 *)
%o (Magma) [(2^n-1)*(3^n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 05 2011
%o (PARI) for(n=0,30, print1((2^n-1)*(3^n-1), ", ")) \\ _G. C. Greubel_, Jan 29 2018
%Y Cf. A000225, A024023.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jan 29 2001