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

Author

N. J. A. Sloane, Nov 13 2003

Keywords

• nonn

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 iDavid Callan, Oct 24 2004

Examples

			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 +...
		

Extensions

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