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A138772
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Number of entries in the second cycles of all permutations of {1,2,...,n}; each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
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2
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0, 1, 5, 27, 168, 1200, 9720, 88200, 887040, 9797760, 117936000, 1536796800, 21555072000, 323805081600, 5187108326400, 88268019840000, 1590132031488000, 30233431388160000, 605024315191296000, 12711912992722944000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=Sum(k*A138771(n,k),k=0..n-1).
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FORMULA
| a(n)=(1/4)(n-1)!(n-1)(n+2). Rec. rel: a(n)=(n+1)a(n-1)+(n-2)! Rec. rel: a(n)=(n-1)a(n-1)+n!/2
E.g.f. if offset 0: x*(2-x)/(2*(1-x)^3). Such e.g.f computations resulted from e-mail exchange with Gary Detlefs. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 27 2010]
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EXAMPLE
| a(3)=5 because the number of entries in the second cycles of (1)(2)(3), (1)(23), (132), (12)(3), (123) and (13)(2) is 1+2+0+1+0+1=5.
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MAPLE
| seq((1/4)*factorial(n-1)*(n-1)*(n+2), n = 1 .. 20);
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CROSSREFS
| Cf. A138771.
Sequence in context: A153233 A084076 A081924 * A082425 A202248 A109963
Adjacent sequences: A138769 A138770 A138771 * A138773 A138774 A138775
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 10 2008
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