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Search: id:A092691
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| A092691 |
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n!*(Sum_{0<2k<=n} 1/(2k)). |
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+0
4
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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
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 3.3.13.
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FORMULA
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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.yu), Mar 06 2004
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EXAMPLE
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a(4)=4!*(1/2+1/4)=18, a(5)=5!*(1/2+1/4)=90.
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PROGRAM
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(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
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Cf. A046674(n)=a(2n).
Sequence in context: A006568 A088336 A133594 this_sequence A064671 A058409 A125833
Adjacent sequences: A092688 A092689 A092690 this_sequence A092692 A092693 A092694
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 04 2004
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