%I A005133 M3320
%S A005133 1,1,4,8,5,22,42,40,120,265,286,764,1729,2198,5168,12144,17034,37702,
%T A005133 88958,136584,288270,682572,1118996,2306464,5428800,9409517,19103988,
%U A005133 44701696,80904113,163344502,379249288,711598944,1434840718,3308997062,
               6391673638,12921383032,29611074174,58602591708,119001063028,271331133136,
               547872065136,1119204224666,2541384297716,5219606253184,10733985041978,
               24300914061436,50635071045768,104875736986272,236934212877684,499877970985660
%N A005133 Number of index n subgroups of modular group PSL_2(Z).
%C A005133 Equivalently, the number of isomorphism class of transitive PSL_2(Z) 
               actions on a finite dotted set of size n. Also the number of different 
               connected dotted trivalent diagrams of size n. - Samuel Alexandre 
               Vidal (samuel.vidal(AT)free.fr), Jul 23 2006
%C A005133 Connected and dotted version of A121352. Dotted version of A121350. Unlabeled 
               version of A121356. Unlabeled and dotted version of A121355. - Samuel 
               Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006
%D A005133 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005133 Newman, Morris; Asymptotic formulas related to free products of cyclic 
               groups. Math. Comp. 30 (1976), no. 136, 838-846.
%H A005133 <a href="Sindx_Gre.html#groups_modular">Index entries for sequences related 
               to modular groups</a>
%H A005133 S. A. Vidal, Sur la Classification et le Denombrement des Sous-groupes 
               du Groupe Modulaire et de leurs Classes de Conjugaison (in French), 
               2006, <a href="http://arXiv.org/abs/math.CO/0702223">http://arXiv.org/
               abs/math.CO/0702223</a>
%F A005133 a(n) = A121355(n)/(n-1)!, a(n) = A121356(n)/n!. - Samuel Alexandre Vidal 
               (samuel.vidal(AT)free.fr), Jul 23 2006
%F A005133 If A(z) = g.f. of a(n) and B(z) = g.f. of A121356 then A(z) = Borel transform 
               of B(z). - Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 
               23 2006
%p A005133 N := 100 : exs2:=sort(convert(taylor(exp(t+t^2/2),t,N+1),polynom),t, 
               ascending) : exs3:=sort(convert(taylor(exp(t+t^3/3),t,N+1),polynom),
               t, ascending) : exs23:=sort(add(op(n+1,exs2)*op(n+1,exs3)/(t^n/ n!),
               n=0..N),t, ascending) : logexs23:=sort(convert(taylor(log(exs23),
               t,N+1),polynom),t, ascending) : sort(add(op(n,logexs23)*n,n=1..N),
               t, ascending) ; - Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), 
               Jul 23 2006
%Y A005133 Cf. A121357.
%Y A005133 Sequence in context: A021677 A124193 A011366 this_sequence A155741 A063808 
               A081455
%Y A005133 Adjacent sequences: A005130 A005131 A005132 this_sequence A005134 A005135 
               A005136
%K A005133 nonn,nice,easy
%O A005133 1,3
%A A005133 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005133 More terms from Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 
               23 2006
%E A005133 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jul 25 2006