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A038076 Number of rooted identity trees with 3-colored leaves. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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-Fran├žois Alcover, Mar 01 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A004111, A038075.

Sequence in context: A119460 A095356 A123104 * A123286 A132818 A134068

Adjacent sequences:  A038073 A038074 A038075 * A038077 A038078 A038079

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified February 26 12:43 EST 2020. Contains 332280 sequences. (Running on oeis4.)