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A045742 Number of interior faces in all noncrossing connected graphs on n nodes on a circle. 2
0, 1, 13, 141, 1456, 14778, 149031, 1499773, 15089932, 151927854, 1531242362, 15451614738, 156114597744, 1579223536788, 15993825704427, 162159485143581, 1645827425223220, 16720488433727910, 170023231905932790 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..200

FORMULA

a(n) = Sum_{k=1..n-2} k*binomial(n+k-2, k)*binomial(3*n-3, n-2-k)/(n-1).

a(n) = Sum_{k=1..n-2} k*A089434(n,k). - Andrew Howroyd, Nov 12 2017

MAPLE

A045742 := proc(n)

        binomial(3*n-3, n-3)*hypergeom([n, 3 - n], [2*n + 1], -1) ;

        simplify(%) ;

end proc: # R. J. Mathar, Mar 27 2012

MATHEMATICA

Rest[Table[Sum[(k Binomial[n+k-2, k]Binomial[3n-3, n-2-k])/(n-1), {k, n-2}], {n, 20}]] (* Harvey P. Dale, Nov 29 2011 *)

PROG

(PARI) a(n) = if(n>1, sum(k=1, n-2, k*binomial(n+k-2, k)*binomial(3*n-3, n-2-k))/(n-1)); \\ Andrew Howroyd, Nov 12 2017

CROSSREFS

Cf. A089434.

Sequence in context: A157160 A263480 A210766 * A122011 A221103 A239250

Adjacent sequences:  A045739 A045740 A045741 * A045743 A045744 A045745

KEYWORD

nonn

AUTHOR

Emeric Deutsch

STATUS

approved

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Last modified August 4 10:56 EDT 2021. Contains 346447 sequences. (Running on oeis4.)