A121797 Number of dissimilar forests on n nodes.

1, 1, 1, 3, 7, 21, 63, 203, 655, 2225, 7519, 26279, 91601, 326873, 1162873, 4215645, 15229413, 55842223, 204204265, 755626769, 2788876167, 10398436275, 38671589327, 145061791275, 542955212801, 2047149292105, 7702710310237

Offset

0,4

Links

T. D. Noe, Table of n, a(n) for n=0..200

Philippe Flajolet, Éric Fusy, Xavier Gourdon, Daniel Panario and Nicolas Pouyanne, A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, arXiv:math.CO/0606370

Formula

G.f.: Product_{n=1..infinity} (1+T_n x^n), where T_n (A000108) has g.f. (1-sqrt(1-4x))/2. - T. D. Noe, Oct 08 2006

Mathematica

nn=200; t=Rest[CoefficientList[Series[1-Sqrt[1-4x]/2, {x, 0, nn}], x]]; CoefficientList[Series[Product[(1+t[[k]]*x^k), {k, nn}], {x, 0, nn}], x] (* T. D. Noe, Oct 08 2006 *)

Crossrefs

Sequence in context: A148673 A141495 A151412 * A109361 A052805 A148674

Adjacent sequences: A121794 A121795 A121796 * A121798 A121799 A121800

Keyword

nonn

Author

N. J. A. Sloane, Oct 08 2006

Extensions

More terms from T. D. Noe, Oct 08 2006

Status

approved