A088342 Let T = Sum_{k >= 1} k^(k-1)*x^k be the g.f. for rooted labeled trees (A000169); sequence has g.f. T/(1-T).

1, 3, 14, 93, 837, 9742, 140449, 2420297, 48506250, 1107465929, 28354713349, 804166591614, 25016362993529, 846770894729841, 30978110173770106, 1217913727100939785, 51206137142679936933, 2292551430448659630790, 108888041255668778897857, 5468436908124359403377993

Offset

1,2

Comments

a(n)=number of forests of rooted trees on [n] whose vertex sets partition [n] into intervals of integers, that is, such that if i<j<k and i,k are vertices in the same component tree, then so is j. For example with n=3, a(n)=14 counts all (n+1)^(n-1)=16 rooted forests on [3] except the 2 forests consisting of a rooted tree on vertex set {1,3} and another on vertex set {2}. - David Callan, Oct 24 2004

Links

Table of n, a(n) for n=1..20.

Example

G.f.: A(x) = x + 3*x^2 + 14*x^3 + 93*x^4 + 837*x^5 + 9742*x^6 + 140449*x^7 +...
such that A(x) = T(x)/(1 - T(x)), where
T(x) = x + 2*x^2 + 9*x^3 + 64*x^4 + 625*x^5 + 7776*x^6 +...+ k^(k-1)*x^k +...

Crossrefs

Sequence in context: A078456 A195134 A089462 * A358118 A364629 A074531

Adjacent sequences: A088339 A088340 A088341 * A088343 A088344 A088345

Keyword

nonn

Author

N. J. A. Sloane, Nov 13 2003

Extensions

Name changed slightly to match offset of 1 by Paul D. Hanna, Oct 23 2016.

Status

approved