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A060150
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a(0) = 1; for n > 0, binomial(2n-1, n-1)^2.
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9
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1, 1, 9, 100, 1225, 15876, 213444, 2944656, 41409225, 590976100, 8533694884, 124408576656, 1828114918084, 27043120090000, 402335398890000, 6015361252737600, 90324408810638025, 1361429497505672100, 20589520178326522500, 312321918272897610000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of square lattice walks that start at (0,0) and end at (1,0) after 2n-1 steps, free to pass through (1,0) at intermediate steps. - S. R. Finch (Steven.Finch(AT)inria.fr), Dec 20 2001
Number of paths of length n connecting two neighboring nodes in optimal chordal graph of degree 4, G(2*d(G)^2+2*d(G)+1,2d(G)+1), of diameter d(G). - B. Dubalski (dubalski(AT)atr.bydgoszcz.pl), Feb 05 2002
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REFERENCES
| R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 1994 Addison-Wesley company, Inc.
A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (5.1.29.2)
K. A. Ross and C. R. B. Wright, Discrete Mathematics, 1992 Prentice Hall Inc.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
R. Bacher, Meander algebras
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FORMULA
| G.f.: 1+(1/AGM(1, sqrt(1-16*x))-1)/4. - Michael Somos, Dec 12, 2002
G.f. = 1+(K(16x)-1)/4 = 1+Sum_{k>0} q^k/(1+q^(2k)) where K(16x) is complete Elliptic integral of first kind at 16x=k^2 and q is the nome. - Michael Somos, May 09, 2005
G.f.: 1+ x*3F2( (1, 3/2, 3/2); (2, 2))(16*x) [From Olivier Gerard (olivier.gerard(AT)gmail.com), Feb 16 2011]
E.g.f. Sum_{n>0} a(n)*x^(2n-1)/(2n-1)! = BesselI(0, 2x)*BesselI(1, 2x) . - Michael Somos Jun 22 2005
a(n)=(n*C(n-1)/2)^2; for n = 1, 3, 5, ..., 2*d(G)-1; when n even a(n)=0; C - Catalan number - B. Dubalski (dubalski(AT)atr.bydgoszcz.pl), Feb 05 2002
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EXAMPLE
| a(9)=9^2*C(4)=9^2*14^2=15876
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PROG
| (PARI) a(n)=if(n<1, n==0, binomial(2*n-1, n-1)^2)
(PARI) { for (n=0, 200, if (n==0, a=1, a=binomial(2*n - 1, n - 1)^2); write("b060150.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 02 2009]
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CROSSREFS
| a(n)=A002894(n)/4, n>0.
Sequence in context: A065736 A092936 A056002 * A202833 A174509 A103461
Adjacent sequences: A060147 A060148 A060149 * A060151 A060152 A060153
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 10 2001
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