A006183 a(n) = (n+1)*a(n-1) + (2-n)*a(n-2). (Formerly M1663)

1, 2, 6, 22, 98, 522, 3262, 23486, 191802, 1753618, 17755382, 197282022, 2387112466, 31249472282, 440096734638, 6635304614542, 106638824162282, 1819969265702946, 32873194861759462, 626524419718239158, 12565295306571352002, 264532532769923200042

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..22.

F. C. Holroyd and W. J. G. Wingate, Cycles in the complement of a tree or other graph, Discrete Math., 55 (1985), 267-282.

Formula

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

Mathematica

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 *)

Prog

(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

Crossrefs

Equals A030297(n-1) - A030297(n-2) + 1. Cf. A054096.

Equals 2 * A001339(n+2).

Sequence in context: A177389 A130907 A054096 * A189844 A189282 A318974

Adjacent sequences: A006180 A006181 A006182 * A006184 A006185 A006186

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from James A. Sellers, Aug 21 2000

a(1) from Robert G. Wilson v, Jun 15 2013

a(21)-a(22) from Vincenzo Librandi, Mar 06 2016

Status

approved