OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
FORMULA
a(n) = Sum_{k=0..n} A144207(n,k).
a(n) ~ c * n^(n-1), where c = 0.762590842281789937101466... . - Vaclav Kotesovec, Sep 10 2014
EXAMPLE
a(3) = 2, because there are 2 simple graphs on 3 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3:
.1.2. .1-2.
..... .|/..
.3... .3...
MAPLE
T:= proc(n, k) option remember; if k=0 then 1 elif k<0 or n<k then 0 elif k=n then binomial(n-1, 2) *n^(n-3) else T(n-1, k) +add(binomial(n-1, j) * T(j+1, j+1) *T(n-1-j, k-j-1), j=2..k-1) fi end: a:= n-> add(T(n, k), k=0..n): seq(a(n), n=0..23);
MATHEMATICA
T[n_, k_] := T[n, k] = Which[k == 0, 1, k<0 || n<k, 0, k == n, Binomial[n-1, 2] *n^(n-3), True, T[n-1, k] + Sum[Binomial[n-1, j] * T[j+1, j+1] * T[n-1-j, k-j-1], {j, 2, k-1}]]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 14 2008
STATUS
approved