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A000305
Number of certain rooted planar maps.
(Formerly M3543 N1435)
2
1, 4, 18, 89, 466, 2537, 14209, 81316, 473338, 2793454, 16674417, 100487896, 610549829, 3735850007, 23000055178, 142370597601, 885521350882, 5531501612071, 34686798239678, 218273864005214, 1377897874711437
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
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
KEYWORD
nonn
EXTENSIONS
More terms from Emeric Deutsch, Mar 03 2004
STATUS
approved