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A038075 Number of rooted identity trees with 2-colored leaves. 3
2, 2, 3, 7, 16, 41, 110, 304, 858, 2474, 7234, 21418, 64057, 193277, 587531, 1797817, 5532916, 17115442, 53186682, 165958893, 519764706, 1633331926, 5148420607, 16273962742, 51574291758, 163834983761, 521597902077, 1663993969029, 5318540288800, 17029516243797 (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 = 3.3683668081969694736300401764..., c = 0.4229796097587478606873477... . - Vaclav Kotesovec, Sep 10 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, 2*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, 2*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, A038076.

Sequence in context: A152255 A002848 A032257 * A032236 A128776 A117387

Adjacent sequences:  A038072 A038073 A038074 * A038076 A038077 A038078

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)