A298539 Number of unlabeled rooted trees with n vertices such that every branch of the root has a different number of nodes.

1, 1, 1, 3, 6, 15, 35, 89, 218, 571, 1446, 3834, 10003, 26864, 71120, 193602, 519409, 1423539, 3865590, 10666555, 29185905, 81078369, 223367624, 623192655, 1727907182, 4840616872, 13482957335, 37923616139, 106070402639, 299214369115, 840217034149

Offset: 1

Author

Gus Wiseman, Jan 21 2018

Keywords

• nonn

Examples

			The a(5) = 6 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), (o((o))), (o(oo)).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000081, A004111, A032305, A290689, A298422, A298533, A298535, A298537, A298539.

Programs

Mathematica

nn=20;
r[n_]:=r[n]=If[n===1,1,Sum[Product[Binomial[r[x]+Count[ptn,x]-1,Count[ptn,x]],{x,Union[ptn]}],{ptn,IntegerPartitions[n-1]}]];
Table[SeriesCoefficient[Product[1+r[n]x^n,{n,nn}],{x,0,n}],{n,0,nn}]

Formula

G.f.: Product_{n>0} (1 + A000081(n) x^n).