%I A002802 M4724 N2019
%S A002802 1,10,70,420,2310,12012,60060,291720,1385670,6466460,29745716,135207800,
%T A002802 608435100,2714556600,12021607800,52895074320,231415950150,1007340018300,
%U A002802 4365140079300,18839025605400,81007810103220,347176329013800,1483389769422600
%N A002802 (2*n+3)!/(6*n!*(n+1)!).
%C A002802 For n >= 1 a(n) is also the number of rooted bicolored unicellular maps 
               of genus 1 on n+2 edges. - Ahmed Fares (ahmedfares(AT)my-deja.com), 
               Aug 20 2001
%C A002802 a(n)=A051133(n+1)/3 =A000911(n)/6. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 02 2007
%D A002802 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002802 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002802 Alain Goupil and Gilles Schaeffer, Factoring N-Cycles and Counting Maps 
               of Given Genus . Europ. J. Combinatorics (1998) 19 819-834.
%D A002802 C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 449.
%D A002802 T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. I, J. 
               Comb. Theory, B, 13, No.3 (1972), 192-218 (Tab.1).
%F A002802 G.f.: (1 - 4*x)^(-5/2).
%F A002802 Asymptotic expression for a(n) is a(n) ~ (n+2)^(3/2) * 4^(n+2) / (sqrt(Pi) 
               * 48)
%F A002802 a(n) = Sum (a+b+c+d+e=n, f(a)*f(b)*f(c)*f(d)*f(e)) with f(n)=binomial(2n, 
               n)=A000984(n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 22 
               2004
%F A002802 a(n-1)=1/4*sum(k=1, n, k*(k+1)*binomial(2*k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 20 2004
%p A002802 with(combinat):for n from 2 to 24 do printf(`%d, `,n*sum(binomial(2*n, 
               n)/12, k=2..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 13 2007
%p A002802 with(combinat):a:=n->sum(sum(numbcomp(2*n,n)/6, j=2..n),k=1..n): seq(a(n), 
               n=2..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 
               2007
%t A002802 a[n_]:=(2*n+3)!/(6*n!*(n+1)!); [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 13 2008]
%Y A002802 Cf. A035309, A000108 (for genus 0 maps).
%Y A002802 Sequence in context: A025221 A005567 A073391 this_sequence A101029 A122892 
               A125347
%Y A002802 Adjacent sequences: A002799 A002800 A002801 this_sequence A002803 A002804 
               A002805
%K A002802 nonn,easy
%O A002802 0,2
%A A002802 N. J. A. Sloane (njas(AT)research.att.com).