Search: id:A000240
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%I A000240 M2763 N1111
%S A000240 1,0,3,8,45,264,1855,14832,133497,1334960,14684571,176214840,2290792933,
%T A000240 32071101048,481066515735,7697064251744,130850092279665,2355301661033952,
%U A000240 44750731559645107,895014631192902120,18795307255050944541,413496759611120779880
%N A000240 Rencontres numbers: permutations with exactly one fixed point.
%D A000240 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000240 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000240 S. K. Das and N. Deo, Rencontres graphs: a family of bipartite graphs, 
               Fib. Quart., Vol. 25, No. 3, August 1987, 250-262.
%D A000240 I. Kaplansky, Symbolic solution of certain problems in permutations, 
               Bull. Amer. Math. Soc., 50 (1944), 906-914.
%D A000240 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               65.
%H A000240 T. D. Noe, <a href="b000240.txt">Table of n, a(n) for n=1..100</a>
%F A000240 E.g.f. = exp(-x)*(1+x^3)/(1-x)(1-x^2). a(n)=sum((-1)^k*n!/k!, k=0..n-1).
%F A000240 a(n) = n*a(n-1)-(-1)^n*n = A000166(n)-(-1)^n = n*A000166(n-1) = A000387(n+1)*2/
               (n+1) = A000449(n+2)*6/((n+1)*(n+2))
%F A000240 G.f.: exp(-x)/(1-x)*x . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 03 2009]
%e A000240 a(3)=3 because the permutations of (1,2,3) with one fixed point are (1,
               3,2), (3,2,1) and (2,1,3)
%p A000240 a:=n->sum(n!*sum((-1)^k/k!, j=0..n), k=0..n): seq(a(n), n=0..21); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 17 2007
%p A000240 restart: G(x):=exp(-x)/(1-x)*x: 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=1..22);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 03 2009]
%t A000240 Table[Subfactorial[n]*(n + 1), {n, 0, 21}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 10 2009]
%Y A000240 Cf. A008290, A000166, A000387, etc.
%Y A000240 A diagonal of A008291.
%Y A000240 Sequence in context: A074435 A039647 A071533 this_sequence A132103 A040018 
               A019016
%Y A000240 Adjacent sequences: A000237 A000238 A000239 this_sequence A000241 A000242 
               A000243
%K A000240 nonn,easy,nice
%O A000240 1,3
%A A000240 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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