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A002690
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(n+1) * (2*n)! / n!.
(Formerly M3665 N1491)
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2
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1, 4, 36, 480, 8400, 181440, 4656960, 138378240, 4670265600, 176432256000, 7374868300800, 337903056691200, 16838835658444800, 906706535454720000, 52459449551308800000, 3245491278907637760000, 213796737998040637440000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Coefficients of orthogonal polynomials.
E.g.f. for series with alternating signs: x/(1+4*x)^(1/2).
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REFERENCES
| H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.
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).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
| E.g.f.: (1-2*x)/(1-4*x)^(3/2).
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MAPLE
| 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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MATHEMATICA
| Table[((n+1)(2n)!)/n!, {n, 0, 20}] (* From Harvey P. Dale, Sep 04 2011 *)
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PROG
| (PARI) a(n)=(n+1)*(2*n)!/n!
(MAGMA) [(n+1) * Factorial(2*n) /Factorial(n): n in [0..20]]; // Vincenzo Librandi, Sep 05 2011
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CROSSREFS
| a(n) = (n+1) * A001813(n) = 2^n * A001193(n+1).
Cf. A002691, A000407.
Sequence in context: A009533 A135906 A197446 * A094417 A138435 A008546
Adjacent sequences: A002687 A002688 A002689 * A002691 A002692 A002693
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by R. Stephan, Mar 21 2004
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