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A000475
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Rencontres numbers: permutations with exactly 4 fixed points.
(Formerly M4969 N2132)
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9
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1, 0, 15, 70, 630, 5544, 55650, 611820, 7342335, 95449640, 1336295961, 20044438050, 320711010620, 5452087178160, 98137569209940, 1864613814984984, 37292276299704525, 783137802293789040, 17229031650463366195, 396267727960657413630
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,3
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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=4..100
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FORMULA
| a(n)=sum((-1)^j*n!/(4!*j!), j=2..n-4).
a(n) = A000166(n)*binomial(n+4, 4). - Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), Nov 08, 2001
EGF:(exp(-x)/(1-x))(x^4/4!). In genaral, for k fixed points:(exp(-x)/(1-x))(x^k/k!). [From Wenjin Woan (wjwoan(AT)hotmail.com), Nov 22 2008]
G.f.: exp(-x)/(1-x)*(x^4/4!) [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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MAPLE
| a:=n->sum(n!*sum((-1)^k/(k-3)!, j=0..n), k=3..n): seq(-a(n)/4!, n=3..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2007
restart: G(x):=exp(-x)/(1-x)*(x^4/4!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=4..23); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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MATHEMATICA
| Table[Subfactorial[n - 4]*Binomial[n, 4], {n, 4, 23}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
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CROSSREFS
| Cf. A000240, A000387, A000449.
A diagonal of A008291.
Sequence in context: A124893 A126402 A053134 * A145053 A168298 A126274
Adjacent sequences: A000472 A000473 A000474 * A000476 A000477 A000478
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula corrected by Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 26 2010
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