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Search: id:A000387
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| A000387 |
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Rencontres numbers: permutations with exactly two fixed points.
(Formerly M4138 N1716)
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+0
12
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| 1, 0, 6, 20, 135, 924, 7420, 66744, 667485, 7342280, 88107426, 1145396460, 16035550531, 240533257860, 3848532125880, 65425046139824, 1177650830516985, 22375365779822544, 447507315596451070, 9397653627525472260, 206748379805560389951
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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Also: odd permutations of length n with no fixed points. - Martin Wohlgemuth (mail(AT)matroid.com), May 31 2003
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 65.
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LINKS
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M. Wohlgemuth Derangements revisited
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FORMULA
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a(n) = sum((-1)^j*n!/(2!*j!), j=2..n-2)
a(n) = A000166(n-2)*binomial(n, 2). - David Wasserman (wasserma(AT)spawar.navy.mil), Aug 13 2004
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MAPLE
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a:=n->sum(n!*sum((-1)^k/(k-1)!, j=0..n), k=1..n): seq(-a(n)/2!, n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 18 2007
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CROSSREFS
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Cf. A000240, A000449, A000475.
A diagonal of A008291.
a(n)+A0003221(n)=A000166(n).
Sequence in context: A074013 A114959 A000386 this_sequence A027148 A095854 A027268
Adjacent sequences: A000384 A000385 A000386 this_sequence A000388 A000389 A000390
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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