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A001392
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9*binomial(2n,n-4)/(n+5).
(Formerly M4637 N1981)
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24
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1, 9, 54, 273, 1260, 5508, 23256, 95931, 389367, 1562275, 6216210, 24582285, 96768360, 379629720, 1485507600, 5801732460, 22626756594, 88152205554, 343176898988, 1335293573130, 5193831553416, 20198233818840, 78542105700240, 305417807763705
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OFFSET
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4,2
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COMMENTS
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Number of n-th generation vertices in the tree of sequences with unit increase labeled by 8 (cf. Zoran Sunik reference) - Benoit Cloitre, Oct 07 2003
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=4. - Herbert Kociemba, May 24 2004
Number of standard tableaux of shape (n+4,n-4). - Emeric Deutsch, May 30 2004
a(n) = A214292(2*n-1,n-5) for n > 4. - Reinhard Zumkeller, Jul 12 2012
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REFERENCES
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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).
Zoran Sunik, Self describing sequences and the Catalan family tree, Elect. J. Combin., 10 (No. 1, 2003).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 4..200
R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
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FORMULA
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Expansion of x^4*C^9, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for 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>=8, a(n-4)=(-1)^(n-8)*coeff(charpoly(A,x),x^8). [Milan Janjic, Jul 08 2010]
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MATHEMATICA
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Table[9*Binomial[2n, n-4]/(n+5), {n, 4, 30}] (* Harvey P. Dale, Mar 03 2011 *)
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PROG
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(PARI) a(n)=9*binomial(n+n, n-4)/(n+5) \\ Charles R Greathouse IV, Jul 31 2011
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CROSSREFS
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First differences are in A026015.
A diagonal of any of the essentially equivalent arrays A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
Cf. A000108, A000245, A002057, A000344, A003517, A000588, A003518, A003519.
Sequence in context: A169796 A027472 A022637 * A188428 A079764 A079761
Adjacent sequences: A001389 A001390 A001391 * A001393 A001394 A001395
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Harvey P. Dale, Mar 03 2011.
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STATUS
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approved
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