A245747 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 2.

1, 2, 5, 10, 21, 42, 87, 178, 371, 773, 1630, 3447, 7346, 15712, 33790, 72922, 158020, 343494, 749101, 1638102, 3591723, 7893801, 17387930, 38379199, 84875595, 188036829, 417284180, 927469844, 2064465340, 4601670624, 10270463564, 22950838754, 51346678940

Offset: 4

Author

Joerg Arndt and Alois P. Heinz, Jul 31 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000

Crossrefs

Column k=2 of A244523.

Programs

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> b(n-1$2, 2$2) -b(n-1$2, 1$2):
seq(a(n), n=4..60);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k], j]*b[n-i*j, i-1, t - j, k], {j, 0, Min[t, n/i]}]]];
a[n_] :=  b[n-1, n-1, 2, 2] - b[n-1, n-1, 1, 1];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

Formula

a(n) = A063895(n+1)-1.