Search: id:A000475
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%I A000475 M4969 N2132
%S A000475 1,0,15,70,630,5544,55650,611820,7342335,95449640,1336295961,20044438050,
%T A000475 320711010620,5452087178160,98137569209940,1864613814984984,37292276299704525,
%U A000475 783137802293789040,17229031650463366195,396267727960657413630
%N A000475 Rencontres numbers: permutations with exactly 4 fixed points.
%D A000475 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000475 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000475 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               65.
%F A000475 a(n)=sum((-1)^j*n!/(4!*j!), j=2..n-4).
%F A000475 a(n) = A000166(n)*binomial(n+3, 3). - Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), 
               Nov 08, 2001
%F A000475 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]
%F A000475 G.f.: exp(-x)/(1-x)*(x^4/4!) [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 03 2009]
%p A000475 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
%p A000475 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]
%t A000475 Table[Subfactorial[n - 4]*Binomial[n, 4], {n, 4, 23}] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
%Y A000475 Cf. A000240, A000387, A000449.
%Y A000475 A diagonal of A008291.
%Y A000475 Sequence in context: A124893 A126402 A053134 this_sequence A145053 A126274 
               A053531
%Y A000475 Adjacent sequences: A000472 A000473 A000474 this_sequence A000476 A000477 
               A000478
%K A000475 nonn
%O A000475 4,3
%A A000475 N. J. A. Sloane (njas(AT)research.att.com).

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