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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
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]
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
Sequence in context: A258459 A320547 A022639 * A211830 A322877 A226708
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)