OFFSET
0,1
COMMENTS
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
E. Biondi, L. Divieti, G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35.
Philip Feinsilver and John McSorley, Zeons, Permanents, the Johnson Scheme, and Generalized Derangements, International Journal of Combinatorics, Volume 2011, Article ID 539030, 29 pages; doi:10.1155/2011/539030.
FORMULA
a(n) = 2 * A082030(n).
a(n) = floor((n+1)*(n+1)!*e) - floor(n*n!*e) [Gary Detlefs, Jun 06 2010]
a(n) = {exp(1)*(n^2+n+1)*n!} for n>0, where {x} is the neareast integer, proposed by Simon Plouffe, March 1993.
G.f.: (1-x)/x/Q(0) -1/x, where Q(k)= 1 - x - x*(k+2)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 22 2013
G.f.: W(0)/x - 1/x, where W(k) = 1 - x*(k+2)/( x*(k+3) - 1/(1 - x*(k+1)/( x*(k+1) - 1/W(k+1) ))); (continued fraction). - Sergei N. Gladkovskii, Aug 26 2013
Conjecture: a(n) +(-n-3)*a(n-1) +(n-1)*a(n-2)=0. - R. J. Mathar, May 03 2017
MATHEMATICA
nn = 20; Range[0, nn]! CoefficientList[Series[2*Exp[x]/(1 - x)^3, {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Error in description corrected Jan 30 2008
More terms from N. J. A. Sloane, Jan 30 2008
STATUS
approved