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A002674
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(2*n)!/2.
(Formerly M4879 N2092)
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8
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1, 12, 360, 20160, 1814400, 239500800, 43589145600, 10461394944000, 3201186852864000, 1216451004088320000, 562000363888803840000, 310224200866619719680000, 201645730563302817792000000, 152444172305856930250752000000, 132626429906095529318154240000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Right side of the binomial sum n-> sum( (-1)^i * (n-i)^(2*n) * binomial(2*n, i), i=0..n) - Yong Kong (ykong(AT)curagen.com), Dec 28 2000
a(n)is the number of ways to display n distinct flags on n distinct poles and then linearly order all (including any empty) poles. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 16 2009]
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REFERENCES
| A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (4.2.2.33)
H. E. Salzer, Tables of coefficients for obtaining central differences from their derivatives, Journal of Mathematics and Physics, 42 (1963), 162-165.
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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FORMULA
| 4*sinh(x/2)^2 = sum(k>=1, x^(2k)/a(k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 08 2002
E.g.f.: (hypergeom([1/2, 1], [], 4*x)-1)/2 (cf. A090438).
a(n)= n(2n-1)! [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 16 2009]
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MATHEMATICA
| Table[n! Pochhammer[n, n], {n, 0, 10}] [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Dec 16 2009]
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CROSSREFS
| a(n)=A090438(n, 2), n>=1 (first column of (4, 2)-Stirling2 array).
Sequence in context: A012384 A012429 A012631 * A012552 A012385 A012430
Adjacent sequences: A002671 A002672 A002673 * A002675 A002676 A002677
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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