A000305 Number of certain rooted planar maps.

1, 4, 18, 89, 466, 2537, 14209, 81316, 473338, 2793454, 16674417, 100487896, 610549829, 3735850007, 23000055178, 142370597601, 885521350882, 5531501612071, 34686798239678, 218273864005214, 1377897874711437

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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]

Crossrefs

Row sums of A046652.

Programs

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 *)

Extensions

More terms from Emeric Deutsch, Mar 03 2004