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A003519
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10C(2n+1, n-4)/(n+6).
(Formerly M4721)
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22
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1, 10, 65, 350, 1700, 7752, 33915, 144210, 600875, 2466750, 10015005, 40320150, 161280600, 641886000, 2544619500, 10056336264, 39645171810
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OFFSET
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4,2
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COMMENTS
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Number of standard tableaux of shape (n+5,n-4). - Emeric Deutsch, May 30 2004
a(n) = A214292(2*n,n-5) for n > 4. - Reinhard Zumkeller, Jul 12 2012
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REFERENCES
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V. E. Hoggatt, Jr. and M. Bicknell, Catalan and related sequences arising from inverses of Pascal's triangle matrices, Fib. Quart., 14 (1976), 395-405.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=4..20.
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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G.f.=x^4*C(x)^10, 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>=9, a(n-5)=(-1)^(n-9)*coeff(charpoly(A,x),x^9). [From Milan Janjic, Jul 08 2010]
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CROSSREFS
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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 A001392.
Sequence in context: A073381 A092441 A022638 * A056280 A000453 A097791
Adjacent sequences: A003516 A003517 A003518 * A003520 A003521 A003522
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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