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A006605
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Number of modes of connections of 2n points.
(Formerly M2899)
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5
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1, 1, 3, 11, 46, 207, 979, 4797, 24138, 123998, 647615, 3428493, 18356714, 99229015, 540807165, 2968468275, 16395456762, 91053897066, 508151297602, 2848290555562, 16028132445156, 90516256568235, 512831902620465
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
H. N. V. Temperley and D. G. Rogers, A note on Baxter's generalization of the Temperley-Lieb operators, pp. 324-328 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978.
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LINKS
| Plouffe, Simon, Master Thesis, copy at the arXiv site
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FORMULA
| Reference gives explicit formula.
G.f.: A(x) = (1/x)*serreverse(x/G(x)) where G(x) is g.f. of A001006 (Motzkin numbers). G.f. satisfies: A(x)^2 = (1/x)*serreverse( x/(1+x+x^2)^2 ). - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 20 2005
G.f. revogf is 1/2*(-x+1+(-(1+x)*(-1+3*x))^(1/2))*x, Simon Plouffe, Master Thesis, UQAM 1992.
A006605(n) = A026302(n)/(n+1) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 02 2010]
a(n)=1/(2*n+1)*sum(binomial(j,2*j-2-3*n)*binomial(2*n+1,j),j=0...2*n+1), [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Dec 24 2010]
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MAPLE
| series(RootOf(x^2*g^4+x*g^2-g+1, g), x=0, 20); - Mark van Hoeij, Nov 16 2011
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PROG
| (PARI) {a(n)=polcoeff(((1/x)*serreverse(x/(1+x+x^2)^2+x^2*O(x^n)))^(1/2), n)} (Hanna)
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CROSSREFS
| Cf. A001006.
Sequence in context: A151140 A151141 A155134 * A193074 A086521 A046996
Adjacent sequences: A006602 A006603 A006604 * A006606 A006607 A006608
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 20 2005
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