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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

a(n) = A214292(2*n-1,n-6) for n > 5. - Reinhard Zumkeller, Jul 12 2012

REFERENCES

A. Papoulis, A new method of inversion of the Laplace transform, Quart. Applied Math. 14 (1956), 405ff.

J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222.

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

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. 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

-(n+6)*(n-5)*a(n) + 2*n*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Jun 20 2013

CROSSREFS

Sequence in context: A023010 A258459 A022639 * A211830 A226708 A206529

Adjacent sequences:  A000586 A000587 A000588 * A000590 A000591 A000592

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 18 14:09 EDT 2017. Contains 290720 sequences.