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A045743
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Number of noncrossing connected graphs on n nodes on a circle having no triangular faces.
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3
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1, 3, 13, 66, 367, 2164, 13293, 84157, 545270, 3598244, 24100375, 163416748, 1119592052, 7738412716, 53894849437, 377851866954, 2664570714233, 18887568709788, 134501247038230, 961774761388430, 6903072966224220
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listen;
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OFFSET
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2,2
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 2..200
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FORMULA
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a(n) = Sum_{i=0..floor((n-2)/2)} binomial(n-2+i, i)*binomial(3*n-3-i, n-2-2*i)/(n-1).
From Paul D. Hanna, Mar 09 2010: (Start)
G.f. A(x): Let F(x) = 1 + A(x)/x = 1 + x + 3*x^2 + 13*x^3 + 66*x^4 +...
then F(x) satisfies: x*F(x)^4 = (1 - F(x))*(1 - 3*F(x) + F(x)^2). (End)
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1-x*A^4/(1-3*A+A^2)); polcoeff(A, n)} \\ Paul D. Hanna, Mar 09 2010
(PARI) a(n) = if(n>1, sum(i=0, floor(n/2)-1, binomial(n-2+i, i)*binomial(3*n-3-i, n-2-2*i))/(n-1)); \\ Andrew Howroyd, Nov 12 2017
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CROSSREFS
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Column k=0 of A089435.
Cf. A045744.
Sequence in context: A228987 A112807 A219537 * A110530 A142979 A302303
Adjacent sequences: A045740 A045741 A045742 * A045744 A045745 A045746
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch
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STATUS
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approved
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