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1, 2, 10, 76, 764, 9496, 140152, 2390480, 46206736, 997313824, 23758664096, 618884638912, 17492190577600, 532985208200576, 17411277367391104, 606917269909048576, 22481059424730751232, 881687990282453393920
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of tableaux on 2n elements. - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 09 2002
a(n) = number of ways to connect 2n points labeled 1,2,...,2n in a line with 0 or more arcs such that at most one arc leaves each point. For example, with arcs separated by dashes, a(2)=10 counts {} (no arcs), 12, 13, 14, 23, 24, 34, 12-34, 13-24, 14-23. - David Callan (callan(AT)stat.wisc.edu), Sep 18 2007
The Hosoya index H(n) of the n-complete graph K_n is given by H(2n+1) = 0 and H(2n) = a(n) [Eric W. Weisstein, Jul 11 2011]
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REFERENCES
| S. Chowla, The asymptotic behavior of solutions of difference equations, in Proceedings of the International Congress of Mathematicians (Cambridge, MA, 1950), Vol. I, 377, Amer. Math. Soc., Providence, RI, 1952.
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LINKS
| Eric Weisstein's World of Mathematics, Complete Graph
Eric Weisstein's World of Mathematics, Hosoya Index
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FORMULA
| a(n)=sum(k=0, n, C(2n, 2*k)*(2k-1)!!) - Benoit Cloitre, May 01 2003
a(n) = n!*2^n*LaguerreL(n, -1/2, -1/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 10 2003
E.g.f.: cosh(x)*exp(x^2/2) (with interpolated zeros) - Paul Barry, May 26 2003
E.g.f.: exp(x/(1-2*x))/sqrt(1-2*x). [From Paul Barry, Apr 12 2010]
a(n) = (1/sqrt(2*pi))*Int((1+x)^(2*n)*exp(-x^2/2),x,-infinity,infinity). [From Paul Barry, Apr 21 2010]
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MATHEMATICA
| NumberOfTableaux[2n]
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(2*n, 2*k)*prod(i=1, k, 2*i-1))
(PARI) a(n)=if(n<0, 0, n*=2; n!*polcoeff(exp(x+x^2/2+x*O(x^n)), n))
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CROSSREFS
| Cf. A066224.
Sequence in context: A136222 A184356 A124426 * A088500 A195136 A140763
Adjacent sequences: A066220 A066221 A066222 * A066224 A066225 A066226
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 19 2001
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EXTENSIONS
| More terms from Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 09 2002
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