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

1,4

Links

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

Formula

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

Example

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

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}]

Crossrefs

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

Sequence in context: A076375 A190586 A113225 * A209450 A291013 A017924

Adjacent sequences: A298536 A298537 A298538 * A298540 A298541 A298542

Keyword

nonn

Author

Gus Wiseman, Jan 21 2018

Status

approved