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A000589
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11C(2n,n-5)/(n+6).
(Formerly M4797 N2048)
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7
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1, 11, 77, 440, 2244, 10659, 48279, 211508, 904475, 3798795, 15737865, 64512240, 262256280, 1059111900, 4254603804, 17018415216, 67837293986
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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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 (kociemba(AT)t-online.de), May 24 2004
Number of standard tableaux of shape (n+5,n-5). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
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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).
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LINKS
| R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
| Expansion of x^5*C^11, where C = (1-(1-4*x)^(1/2))/(2*x)is g.f. for Catalan numbers, A000108 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 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). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
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CROSSREFS
| Sequence in context: A059625 A023010 A022639 * A118936 A041224 A030054
Adjacent sequences: A000586 A000587 A000588 * A000590 A000591 A000592
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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