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 A000305 Number of certain rooted planar maps. (Formerly M3543 N1435) 3
 1, 4, 18, 89, 466, 2537, 14209, 81316, 473338, 2793454, 16674417, 100487896, 610549829, 3735850007, 23000055178, 142370597601, 885521350882, 5531501612071, 34686798239678, 218273864005214, 1377897874711437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545. W. G. Brown, Enumeration of non-separable planar maps [Annotated scanned copy] MAPLE with(linalg): T := proc(n, k) if k<=n then k*sum((2*j-k+1)*(j-1)!*(3*n-k-j)!/(j-k+1)!/(j-k)!/(2*k-j-1)!/(n-j)!, j=k..min(n, 2*k-1))/(2*n-k+1)! else 0 fi end:A := matrix(30, 30, T): seq(sum(A[i, j], j=1..i), i=1..30); R := RootOf(x-t*(t-1)^2, t); ogf := series((R+1)/((1-R-R^2)*(R-1)^2), x=0, 20); # Mark van Hoeij, Nov 08 2011 MATHEMATICA t[n_, k_] := If[k <= n, k*Sum[(2*j-k+1)*(j-1)!*(3*n-k-j)!/(j-k+1)!/(j-k)!/ (2*k-j-1)!/(n-j)!, {j, k, Min[n, 2*k-1]}]/(2*n-k+1)!, 0]; a[n_] := Sum[ t[n, k], {k, 1, n}]; Array[a, 21] (* Jean-François Alcover, Feb 07 2016 after Herman Jamke in A046652 *) CROSSREFS Row sums of A046652. Sequence in context: A127394 A046984 A129323 * A200029 A020070 A197650 Adjacent sequences:  A000302 A000303 A000304 * A000306 A000307 A000308 KEYWORD nonn AUTHOR EXTENSIONS More terms from Emeric Deutsch, Mar 03 2004 STATUS approved

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