

A048808


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


11



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
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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}] (* JeanFrançois Alcover, May 11 2019, after Alois P. Heinz in A244925 *)


CROSSREFS

Cf. A048809A048816.
Column k=3 of A244925.
Sequence in context: A206290 A091696 A280303 * A263358 A239915 A013983
Adjacent sequences: A048805 A048806 A048807 * A048809 A048810 A048811


KEYWORD

nonn


AUTHOR

Christian G. Bower, Apr 15 1999


STATUS

approved



