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Search: id:A002674
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| A002674 |
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(2*n)!/2.
(Formerly M4879 N2092)
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+0
4
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| 1, 12, 360, 20160, 1814400, 239500800, 43589145600, 10461394944000, 3201186852864000, 1216451004088320000, 562000363888803840000, 310224200866619719680000, 201645730563302817792000000, 152444172305856930250752000000, 132626429906095529318154240000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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REFERENCES
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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.
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FORMULA
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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).
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CROSSREFS
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a(n)=A090438(n, 2), n>=1 (first column of (4, 2)-Stirling2 array).
Adjacent sequences: A002671 A002672 A002673 this_sequence A002675 A002676 A002677
Sequence in context: A012384 A012429 A012631 this_sequence A012552 A012385 A012430
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Simon Plouffe (simon.plouffe(AT)gmail.com)
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