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Search: id:A138772
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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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+0
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
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A138771(n,k),k=0..n-1).
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FORMULA
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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
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EXAMPLE
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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
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seq((1/4)*factorial(n-1)*(n-1)*(n+2), n = 1 .. 20);
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CROSSREFS
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Cf. A138771.
Sequence in context: A153233 A084076 A081924 this_sequence A082425 A109963 A091101
Adjacent sequences: A138769 A138770 A138771 this_sequence A138773 A138774 A138775
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 10 2008
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