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Search: id:A002690
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| A002690 |
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(n+1) * (2n)! / n!.
(Formerly M3665 N1491)
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+0
2
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| 1, 4, 36, 480, 8400, 181440, 4656960, 138378240, 4670265600, 176432256000, 7374868300800, 337903056691200, 16838835658444800, 906706535454720000, 52459449551308800000, 3245491278907637760000, 213796737998040637440000
(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.
E.g.f. for series with alternating signs: x/(1+4x)^(1/2).
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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.: (1-2x)/(1-4x)^(3/2).
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MAPLE
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with(combstruct):bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, labeled], size=n)*n, n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 05 2007
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PROGRAM
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(PARI) a(n)=(n+1)*(2*n)!/n!
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CROSSREFS
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a(n) = (n+1) * A001813(n) = 2^n * A001193(n+1).
Cf. A002691, A000407.
Sequence in context: A136224 A009533 A135906 this_sequence A094417 A138435 A008546
Adjacent sequences: A002687 A002688 A002689 this_sequence A002691 A002692 A002693
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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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