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 A000589 a(n) = 11*binomial(2n,n-5)/(n+6). (Formerly M4797 N2048) 9
 1, 11, 77, 440, 2244, 10659, 48279, 211508, 904475, 3798795, 15737865, 64512240, 262256280, 1059111900, 4254603804, 17018415216, 67837293986, 269638992062, 1069258071970, 4232010895376, 16723268860760, 65997186039785, 260170725132045, 1024713341952300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 COMMENTS Number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) which touch but do not cross the line x-y=5. - Herbert Kociemba, May 24 2004 Number of standard tableaux of shape (n+5,n-5). - Emeric Deutsch, May 30 2004 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 5..200 Richard K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article 00.1.6. Athanasios Papoulis, A new method of inversion of the Laplace transform, Quart. Applied Math. 14 (1956), 405ff. Athanasios Papoulis, A new method of inversion of the Laplace transform, Quart. Appl. Math 14 (1957), 405-414. [Annotated scan of selected pages] John Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222. FORMULA Expansion of x^5*C^11, where C = (1-(1-4*x)^(1/2))/(2*x) is the g.f. for the Catalan numbers, A000108. - Philippe Deléham, Feb 03 2004 Let A be the Toeplitz matrix of order n defined by: A[i,i-1]=-1, A[i,j]=Catalan(j-i), (i<=j), and A[i,j]=0, otherwise. Then, for n>=10, a(n-5)=(-1)^(n-10)*coeff(charpoly(A,x),x^10). - Milan Janjic, Jul 08 2010 a(n) = A214292(2*n-1,n-6) for n > 5. - Reinhard Zumkeller, Jul 12 2012 -(n+6)*(n-5)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jun 20 2013 From Amiram Eldar, Sep 26 2022: (Start) Sum_{n>=5} 1/a(n) = 5993/1540 - 152*Pi/(99*sqrt(3)). Sum_{n>=5} (-1)^(n+1)/a(n) = 210624*log(phi)/(275*sqrt(5)) - 1262077/7700, where phi is the golden ratio (A001622). (End) MATHEMATICA a[n_] := 11*Binomial[2*n, n-5]/(n+6); Array[a, 25, 5] (* Amiram Eldar, Sep 26 2022 *) CROSSREFS Cf. A000108, A001622, A214292. Sequence in context: A258459 A320547 A022639 * A211830 A322877 A226708 Adjacent sequences: A000586 A000587 A000588 * A000590 A000591 A000592 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified November 30 18:31 EST 2023. Contains 367461 sequences. (Running on oeis4.)