%I A003408 M4643
%S A003408 1,9,66,455,3060,20349,134596,888030,5852925,38567100,254186856,
%T A003408 1676056044,11058116888,73006209045,482320623240,3188675231420,
%U A003408 21094923659355,139646485582065,925029565741050,6131164307078475
%N A003408 C(3n+6,n).
%C A003408 Number of connected graphs without crossing edges on n+3 nodes on a circle 
               and having exactly 1 interior face. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Nov 06 2001
%D A003408 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003408 C. Domb and A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 
               9 (1974), 341-358.
%H A003408 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%e A003408 a(0)=1 because among the 4 non-crossing connected graphs on 3 nodes on 
               a circle only the triangle has exactly 1 interior face.
%p A003408 a:=n->sum(binomial(2*n-2,n+j)*binomial(n-1,n-j),j=0..n): seq(a(n), n=3..22); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2007
%Y A003408 Sequence in context: A051375 A081902 A002695 this_sequence A037698 A037607 
               A055148
%Y A003408 Adjacent sequences: A003405 A003406 A003407 this_sequence A003409 A003410 
               A003411
%K A003408 nonn,easy
%O A003408 0,2
%A A003408 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A003408 Formula found by Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A003408 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000