A038075 Number of rooted identity trees with 2-colored leaves.

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

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

G.f. A(x) satisfies: A(x) = 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, 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