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A071724
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3*C(2n,n-1)/(n+2), n>0. a(0)=1.
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5
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1, 1, 3, 9, 28, 90, 297, 1001, 3432, 11934, 41990, 149226, 534888, 1931540, 7020405, 25662825, 94287120, 347993910, 1289624490, 4796857230, 17902146600, 67016296620, 251577050010, 946844533674, 3572042254128, 13505406670700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of standard tableaux of shape (n+1,n-1) (n>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
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FORMULA
| G.f. is (C(x)-1)(1-x)/x = (1+x^2C(x)^3)C(x), where C(x) is g.f. for Catalan numbers, A000108.
G.f.: ((1-sqrt(1-4x))/(2x)-1)(1-x)/x = A(x) satisfies x^2A(x)^2+(x-1)(2x-1)A(x)+(x-1)^2=0.
G.f.=1+xC(x)^3, where C(x) is g.f. for the Catalan numbers (A000108). Sequence without the first term is the 3-fold convolution of the Catalan sequence. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 30 2004
a(n) is the n-th moment of the function defined on the segment (0, 4) of x axis: a(n)= int(x^n*(-x^(1/2)*cos(3*arcsin(1/2*x^(1/2)))/Pi), x=0..4), n=0, 1... . - Karol A. Penson ( penson(AT)lptl.jussieu.fr), Sep 29 2004
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PROG
| (PARI) a(n)=if(n<1, n==0, 3*(2*n)!/(n+2)!/(n-1)!)
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CROSSREFS
| a(n)=A000245(n), n>0.
Cf. A002421.
Sequence in context: A094803 A094826 A033190 * A000245 A143739 A189940
Adjacent sequences: A071721 A071722 A071723 * A071725 A071726 A071727
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2002
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