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

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

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• easy

References

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

Links

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

Crossrefs

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

Equals 2 * A001339(n+2).

Programs

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

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 *)

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

Extensions

More terms from James Sellers, Aug 21 2000

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

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