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A000449
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Rencontres numbers: permutations with exactly 3 fixed points.
(Formerly M4700 N2009)
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8
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1, 0, 10, 40, 315, 2464, 22260, 222480, 2447445, 29369120, 381798846, 5345183480, 80177752655, 1282844041920, 21808348713320, 392550276838944, 7458455259940905, 149169105198816960, 3132551209175157490, 68916126601853463240
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,3
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 65.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=3..100
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FORMULA
| a(n)=sum((-1)^j*n!/(3!*j!), j=2..n-3).
For n >= 3 a(n) = C(n, 3) * A000166(n-3) = 1/6 * n! * sum((-1)^k /k!, k=0..n-3). - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 14 2001
frac 1{e^x\ (1-x)}frac{x^3}6 [From Wenjin Woan (wjwoan(AT)hotmail.com), Nov 20 2008]
Contribution from Weisenhorn Paul (weisenhorn-f.p(AT)online.de), May 30 2010: (Start)
a(n)=binomial(n,3)*A000166(n-3) with 3 fixed-points
a(n)=binomial(n,k)*A000166(n-k) with k fixed-points
(End)
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MAPLE
| a:=n->sum(n!*sum((-1)^k/(k-2)!, j=0..n), k=2..n): seq(a(n)/3!, n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
Contribution from Weisenhorn Paul (weisenhorn-f.p(AT)online.de), May 30 2010: (Start)
with k fixed-points:
G:=exp(-z)*z^k/((1-z)*k!: Gser:=series(G, z, 21):
for n from k to 20 do a(n)=n!*coeff(Gser, z, n): end do:
(End)
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MATHEMATICA
| Table[Subfactorial[n - 3]*Binomial[n, 3], {n, 3, 22}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
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CROSSREFS
| Cf. A000240, A000387, A000475.
A diagonal of A008291.
Sequence in context: A060580 A118266 A054885 * A027274 A016082 A003355
Adjacent sequences: A000446 A000447 A000448 * A000450 A000451 A000452
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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