A038077 Number of rooted identity trees with 2-colored nodes.

2, 4, 10, 36, 132, 532, 2222, 9584, 42248, 189776, 864830, 3989656, 18593424, 87413444, 414060796, 1974260912, 9467922870, 45638482068, 221001289714, 1074591477112, 5244497440468, 25681907242416, 126149132242490, 621386729646752, 3068748094479108

Offset

1,1

Comments

Shifts left and halves under Weigh transform.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

Formula

a(n) = 2 * A005753(n).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> `if`(n=1, 2, 2*b((n-1)$2)):
seq(a(n), n=1..40); # Alois P. Heinz, May 20 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==1, 2, 2*b[n-1, n-1]];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)

Crossrefs

Cf. A004111, A038078, A038079, A038080, A246312.

Sequence in context: A126941 A354963 A188495 * A006396 A192502 A243567

Adjacent sequences: A038074 A038075 A038076 * A038078 A038079 A038080

Keyword

nonn,eigen

Author

Christian G. Bower, Jan 04 1999

Status

approved