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Search: id:A002691
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| A002691 |
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(n+2) * (2n+1) * (2n-1)! / (n-1)!.
(Formerly M4661 N1996)
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+0
2
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| 1, 9, 120, 2100, 45360, 1164240, 34594560, 1167566400, 44108064000, 1843717075200, 84475764172800, 4209708914611200, 226676633863680000, 13114862387827200000, 811372819726909440000, 53449184499510159360000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Coefficients of orthogonal polynomials.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.
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FORMULA
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E.g.f.: (1-x)/(1-4x)^(5/2).
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MAPLE
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a:=n->sum((count(Permutation(n*2-1), size=n)), j=0..n)/2: seq(a(n), n=1..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007
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PROGRAM
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(PARI) a(n)=(n+2)*(2*n+1)*(2*n-1)!/(n-1)!
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CROSSREFS
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Cf. A002690.
Sequence in context: A061172 A167593 A024487 this_sequence A157930 A017102 A167722
Adjacent sequences: A002688 A002689 A002690 this_sequence A002692 A002693 A002694
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by R. Stephan, Mar 21 2004
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