A245750 Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 5.

1, 7, 26, 91, 291, 885, 2588, 7373, 20555, 56413, 152812, 409696, 1089029, 2874506, 7542257, 19690939, 51188137, 132579401, 342294012, 881292334, 2263535926, 5801350565, 14840644204, 37901021924, 96650247055, 246137463494, 626087267035, 1590840361215

Offset

15,2

Links

Alois P. Heinz, Table of n, a(n) for n = 15..1000

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, 5$2) -b(n-1$2, 4$2):
seq(a(n), n=15..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, 5, 5] - b[n-1, n-1, 4, 4];
Table[a[n], {n, 15, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

Crossrefs

Column k=5 of A244523.

Sequence in context: A240256 A372611 A279761 * A268776 A050476 A026617

Adjacent sequences: A245747 A245748 A245749 * A245751 A245752 A245753

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 31 2014

Status

approved