Search: id:A060150
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%I A060150
%S A060150 1,1,9,100,1225,15876,213444,2944656,41409225,590976100,8533694884,
%T A060150 124408576656,1828114918084,27043120090000,402335398890000,6015361252737600,
%U A060150 90324408810638025,1361429497505672100,20589520178326522500,312321918272897610000
%N A060150 a(0) = 1; for n > 0, binomial(2n-1, n-1)^2.
%C A060150 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
%C A060150 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
%D A060150 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, 1994 
               Addison-Wesley company, Inc.
%D A060150 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)
%D A060150 K. A. Ross and C. R. B. Wright, Discrete Mathematics, 1992 Prentice Hall 
               Inc.
%H A060150 Harry J. Smith, <a href="b060150.txt">Table of n, a(n) for n=0,...,200</
               a>
%H A060150 R. Bacher, <a href="http://www-fourier.ujf-grenoble.fr/cgi-bin/qau_prep.pl?AutorName=BACHER">
               Meander algebras</a>
%F A060150 G.f.: 1+(1/AGM(1, sqrt(1-16*x))-1)/4. - Michael Somos, Dec 12, 2002
%F A060150 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
%F A060150 E.g.f. Sum_{n>0} a(n)*x^(2n-1)/(2n-1)! = BesselI(0, 2x)*BesselI(1, 2x) 
               . - Michael Somos Jun 22 2005
%F A060150 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
%e A060150 a(9)=9^2*C(4)=9^2*14^2=15876
%o A060150 (PARI) a(n)=if(n<1,n==0,binomial(2*n-1,n-1)^2)
%o A060150 (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]
%Y A060150 a(n)=A002894(n)/4, n>0.
%Y A060150 Sequence in context: A065736 A092936 A056002 this_sequence A103461 A101563 
               A007133
%Y A060150 Adjacent sequences: A060147 A060148 A060149 this_sequence A060151 A060152 
               A060153
%K A060150 nonn,easy
%O A060150 0,3
%A A060150 N. J. A. Sloane (njas(AT)research.att.com), Apr 10 2001

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