OFFSET
0,2
COMMENTS
a(n) is also the number of subtrees of the complete graph K_{n+2} which contain 2 fixed adjacent edges (i.e. a fixed K_{1,2}). For n=2, the a(2)=4 solutions are the 4 subtrees of K_4 which contain 2 fixed adjacent edges (i.e. those 2 edges, 1 copy of K_{1,3}, and 2 copies of P_4). - Kellie J. MacPhee, Jul 25 2013
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
FORMULA
a(n) = Sum_{k=0..n} 3*(n-k+3)^(n-k-1)*C(n, k).
E.g.f.: exp(x)*(-LambertW(-x)/x)^3.
a(n) ~ 3*exp(3+exp(-1))*n^(n-1). - Vaclav Kotesovec, Jul 08 2013
MAPLE
a:= n-> add(3*(n-j+3)^(n-j-1)*binomial(n, j), j=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Oct 30 2012
MATHEMATICA
Table[Sum[3(n-k+3)^(n-k-1) Binomial[n, k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Dec 04 2011 *)
CoefficientList[Series[E^x*(-LambertW[-x]/x)^3, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 08 2013 *)
PROG
(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)*(-lambertw(-x)/x)^3)) \\ G. C. Greubel, Nov 16 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 05 2003
STATUS
approved