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%I M1663 #31 Sep 08 2022 08:44:34
%S 1,2,6,22,98,522,3262,23486,191802,1753618,17755382,197282022,
%T 2387112466,31249472282,440096734638,6635304614542,106638824162282,
%U 1819969265702946,32873194861759462,626524419718239158,12565295306571352002,264532532769923200042
%N a(n) = (n+1)*a(n-1) + (2-n)*a(n-2).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H F. C. Holroyd and W. J. G. Wingate, <a href="http://dx.doi.org/10.1016/S0012-365X(85)80003-0">Cycles in the complement of a tree or other graph</a>, Discrete Math., 55 (1985), 267-282.
%F G.f.: 2*Sum_{k>=0} k!*(x/(1-x))^k - 1 = Q(0) -1, where Q(k)= 1 + 1/(1 - x*(k+1)/(x*(k+1) + (1-x)/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Aug 08 2013
%t RecurrenceTable[{a[n] == (n + 1) a[n - 1] + (2 - n) a[n - 2], a[0] == 1, a[1] == 2}, a, {n, 20}] (* _Robert G. Wilson v_, Jun 15 2013 *)
%o (Magma) [n le 2 select n else n*Self(n-1)+(3-n)*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Mar 06 2016
%Y Equals A030297(n-1) - A030297(n-2) + 1. Cf. A054096.
%Y Equals 2 * A001339(n+2).
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _James A. Sellers_, Aug 21 2000
%E a(1) from _Robert G. Wilson v_, Jun 15 2013
%E a(21)-a(22) from _Vincenzo Librandi_, Mar 06 2016
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