A048808 Number of rooted trees with n nodes with every leaf at height 3.

1, 1, 2, 3, 5, 7, 12, 18, 27, 42, 64, 96, 146, 219, 327, 491, 730, 1084, 1608, 2376, 3500, 5154, 7563, 11076, 16193, 23625, 34395, 50005, 72550, 105089, 151984, 219448, 316362, 455434, 654661, 939736, 1347137, 1928593, 2757449, 3937675

Offset: 4

Author

Christian G. Bower, Apr 15 1999

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 4..10000 (terms 4..1000 from Alois P. Heinz)
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A048809-A048816.

Column k=3 of A244925.

Programs

Mathematica

T[n_, k_] := T[n, k] = If[n == 1, 1, If[k == 0, 0, Sum[Sum[If[d < k, 0, T[d, k - 1]*d], {d, Divisors[j]}]*T[n - j, k], {j, 1, n - 1}]/(n - 1)]];
a[n_] := T[n, 3];
Table[a[n], {n, 4, 50}] (* Jean-François Alcover, May 11 2019, after Alois P. Heinz in A244925 *)

Formula

Euler transform of A002865 (with a(0)=0) shifted right.