OFFSET
1,3
LINKS
M. Bauer and O. Golinelli, On the kernel of tree incidence matrices, J. Integer Sequences, Vol. 3 (2000), #00.1.4.
FORMULA
a(n) = n^(n-1) - 2 * Sum_{m=2..n} (-1)^m * n^(n-m) * m^(m-2)* binomial(n-1, m-1).
G.f. satisfies x^2 + 2*x - x*e^x = Sum_{n >= 1} (a(n)/n!) (x*e^x*e^(-x*e^x))^n.
MATHEMATICA
a[n_] := n^(n - 1) - 2*Sum[(-1)^m*n^(n - m)*m^(m - 2)*Binomial[n - 1, m - 1], {m, 2, n}]; Table[a[n], {n, 1, 18}] (* Jean-François Alcover, Dec 10 2012, from formula *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Michel Bauer (bauer(AT)spht.saclay.cea.fr), Jan 20 2000
EXTENSIONS
More terms from David W. Wilson, Dec 08 2000
STATUS
approved