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A092691
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n!*(Sum_{0<2k<=n} 1/(2k)).
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8
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0, 0, 1, 3, 18, 90, 660, 4620, 42000, 378000, 4142880, 45571680, 586776960, 7628100480, 113020427520, 1695306412800, 28432576972800, 483353808537600, 9056055981772800, 172065063653683200, 3562946373482496000, 74821873843132416000, 1697172166720622592000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Stirling transform of -(-1)^n*a(n-1)=[1,0,1,-3,18,...] is A052856(n-2)=[1,1,2,4,14,76,...].
Number of cycles of even cardinality in all permutations of [n]. Example: a(3)=3 because among (1)(2)(3), (1)(23), (12)(3), (13)(2), (132), (123) we have three cycles of even length. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2004
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 3.3.13.
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LINKS
| N. J. A. Sloane and T. D. Noe, Table of n, a(n) for n = 0..200
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FORMULA
| a(2n+1)=(2n+1)a(2n).
a(n) = n!*(Psi(floor(n/2)+1)+gamma)/2. E.g.f.: ln(1-x^2)/(2*x-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 06 2004
a(n)=n!/2*h(floor(n/2)), where h(n)=sum(1/k,k=1..n).[From Gary Detlefs, Jul 19 2011]
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EXAMPLE
| a(4)=4!*(1/2+1/4)=18, a(5)=5!*(1/2+1/4)=90.
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PROG
| (PARI) a(n)=if(n<0, 0, n!*sum(k=1, n\2, 1/k)/2)
(PARI) {a(n)=if(n<0, 0, n!*polcoeff( log(1-x^2+x*O(x^n))/(2*x-2), n))}
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CROSSREFS
| A046674(n)=a(2n). Cf. A081358, A151883, A151884.
Sequence in context: A147518 A088336 A133594 * A064671 A058409 A125833
Adjacent sequences: A092688 A092689 A092690 * A092692 A092693 A092694
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 04 2004
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