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 A000590 a(n) = 13*binomial(2n,n-6)/(n+7). (Formerly M4908 N2104) 7
 1, 13, 104, 663, 3705, 19019, 92092, 427570, 1924065, 8454225, 36463440, 154969620, 650872404, 2707475148, 11173706960, 45812198536, 186803188858, 758201178306, 3065415516592, 12352414499425, 49634247352235, 198954083924505, 795816335698020, 3177498557750790 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 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=6. - Herbert Kociemba, May 24 2004 Number of standard tableaux of shape (n+6,n-6). - Emeric Deutsch, May 30 2004 a(n) = A214292(2*n-1,n-7) for n > 6. - Reinhard Zumkeller, Jul 12 2012 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 = 6..200 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6. A. Papoulis, A new method of inversion of the Laplace transform, Quart. Applied Math. 14 (1956), 405ff. A. Papoulis, A new method of inversion of the Laplace transform, Quart. Appl. Math 14 (1957), 405-414. [Annotated scan of selected pages] J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222. FORMULA G.f.: x^6*C(x)^13, where C(x)=[1-sqrt(1-4x)]/(2x) is g.f. for the Catalan numbers (A000108). - Emeric Deutsch, May 30 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>=12, a(n-6)=(-1)^(n-12)*coeff(charpoly(A,x),x^12). [Milan Janjic, Jul 08 2010] -(n+7)*(n-6)*a(n) +2*n*(2*n-1)*a(n-1)=0. - R. J. Mathar, Jun 20 2013 PROG (PARI) a(n) = 13*binomial(2*n, n-6)/(n+7); \\ Michel Marcus, Oct 16 2017 CROSSREFS Sequence in context: A282921 A023011 A022641 * A052065 A303967 A304929 Adjacent sequences:  A000587 A000588 A000589 * A000591 A000592 A000593 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 18 07:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)