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

4,3

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

Formula

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

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 *)

Crossrefs

Cf. A048809-A048816.

Column k=3 of A244925.

Sequence in context: A091696 A334683 A280303 * A263358 A239915 A013983

Adjacent sequences: A048805 A048806 A048807 * A048809 A048810 A048811

Keyword

nonn

Author

Christian G. Bower, Apr 15 1999

Status

approved