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A000259 Number of certain rooted planar maps.
(Formerly M2943 N1185)
1
1, 3, 13, 63, 326, 1761, 9808, 55895, 324301, 1908878, 11369744, 68395917, 414927215, 2535523154, 15592255913, 96419104103, 599176447614, 3739845108057, 23435007764606, 147374772979438, 929790132901804 (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

Table of n, a(n) for n=1..21.

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)*(j-1)!*(3*n-j-k-1)!/(j-k)!/(j-k)!/(2*k-j)!/(n-j)!, j=k..min(n, 2*k))/(2*n-k)! else 0 fi end: A := matrix(30, 30, T): seq(sum(A[i, j], j=1..i), i=1..30); # Emeric Deutsch

R := RootOf(x-t*(t-1)^2, t); ogf := series(1/((1-R-R^2)*(R-1)^2), x=0, 30); # Mark van Hoeij, Nov 08 2011

MATHEMATICA

R = Root[#^3-2#^2+#-x&, 1]; CoefficientList[1/((1-R-R^2)*(R-1)^2) + O[x]^30, x] (* Jean-Fran├žois Alcover, Feb 06 2016, after Mark van Hoeij *)

CROSSREFS

Row sums of A046651.

Sequence in context: A001850 A130525 A243280 * A007855 A193112 A192729

Adjacent sequences:  A000256 A000257 A000258 * A000260 A000261 A000262

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Emeric Deutsch, Mar 03 2004

STATUS

approved

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Last modified March 30 04:57 EDT 2017. Contains 284297 sequences.