A038076 Number of rooted identity trees with 3-colored leaves.

3, 3, 6, 16, 46, 142, 461, 1542, 5278, 18417, 65218, 233816, 846938, 3094943, 11395715, 42237936, 157465847, 590075550, 2221391912, 8397223487, 31861406058, 121300625969, 463233477550, 1774034788166, 6811612470692, 26216538077715, 101125406981562

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..600

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Formula

Shifts left under Weigh transform.

a(n) ~ c * d^n / n^(3/2), where d = 4.0814589930714884560076189705..., c = 0.4583632659157592121544633778... . - Vaclav Kotesovec, Sep 06 2014

G.f. A(x) satisfies: A(x) = 2*x + x * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) / k ). - Ilya Gutkovskiy, May 19 2023

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> `if`(n<2, 3*n, b(n-1, n-1)):
seq(a(n), n=1..35);  # Alois P. Heinz, Aug 01 2013

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 3*n, b[n-1, n-1]];
Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)

Crossrefs

Cf. A004111, A038075.

Sequence in context: A348539 A095356 A123104 * A123286 A132818 A134068

Adjacent sequences: A038073 A038074 A038075 * A038077 A038078 A038079

Keyword

nonn

Author

Christian G. Bower, Jan 04 1999

Status

approved