OFFSET
0,2
LINKS
A. Knopfmacher and M. E. Mays, Graph Compositions. I: Basic Enumeration, Integers 1(2001), #A04.
FORMULA
E.g.f.: (-1+exp(x)+exp(2*x))*exp(exp(x)-1).
G.f.: (G(0)*(1-x)-1-x)/x^2 where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 03 2013
G.f.: - G(0)*(1+1/x) where G(k) = 1 - 1/(1-x*(k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 07 2013
G.f.: (Q(0) -1)*(1+x)/x^2, where Q(k) = 1 - x^2*(k+1)/( x^2*(k+1) - (1-x*(k+1))*(1-x*(k+2))/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 10 2013
a(n) = Sum_{k=0..n} Stirling2(n,k) * (k+1)^2. - Ilya Gutkovskiy, Aug 09 2021
MAPLE
with(combinat): a:=n->bell(n+2)-bell(n): seq(a(n), n=0..21); # Zerinvary Lajos, Jul 01 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jan 02 2003
STATUS
approved