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 A003408 a(n) = binomial(3n+6, n). (Formerly M4643) 9
 1, 9, 66, 455, 3060, 20349, 134596, 888030, 5852925, 38567100, 254186856, 1676056044, 11058116888, 73006209045, 482320623240, 3188675231420, 21094923659355, 139646485582065, 925029565741050, 6131164307078475, 40661170824914640, 269807672771096460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of connected graphs without crossing edges on n+3 nodes on a circle and having exactly 1 interior face. - Emeric Deutsch, Nov 06 2001 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 0..200 C. Domb and A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358. C. Domb & A. J. Barrett, Enumeration of ladder graphs, Discrete Math. 9 (1974), 341-358. (Annotated scanned copy) C. Domb & A. J. Barrett, Notes on Table 2 in "Enumeration of ladder graphs", Discrete Math. 9 (1974), 55. (Annotated scanned copy) Milan Janjic, Two Enumerative Functions FORMULA a(n) = Sum_{k=0..n} binomial(2*n+k+5,k). - Arkadiusz Wesolowski, Apr 02 2012 2*n*(n+3)*(2*n+5)*a(n) - 3*(3*n+5)*(3*n+4)*(n+2)*a(n-1) = 0. - R. J. Mathar, Feb 05 2013 EXAMPLE 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. MAPLE 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, Jan 29 2007 R := RootOf(x-t*(t-1)^2, t); ogf := series(1/((1-3*R)*(1-R)^6), x=0, 20); # Mark van Hoeij, Nov 08 2011 MATHEMATICA Table[Binomial[3*n + 6, n], {n, 0, 20}] (* Arkadiusz Wesolowski, Apr 02 2012 *) CROSSREFS Sequence in context: A051375 A081902 A002695 * A037698 A037607 A055148 Adjacent sequences:  A003405 A003406 A003407 * A003409 A003410 A003411 KEYWORD nonn,easy AUTHOR EXTENSIONS Formula found by Simon Plouffe More terms from James A. Sellers, Aug 21 2000 STATUS approved

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Last modified June 23 17:11 EDT 2021. Contains 345402 sequences. (Running on oeis4.)