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Number of rooted trees with n nodes with every leaf at height 3.
11

%I #22 May 15 2019 06:42:40

%S 1,1,2,3,5,7,12,18,27,42,64,96,146,219,327,491,730,1084,1608,2376,

%T 3500,5154,7563,11076,16193,23625,34395,50005,72550,105089,151984,

%U 219448,316362,455434,654661,939736,1347137,1928593,2757449,3937675

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

%H Vaclav Kotesovec, <a href="/A048808/b048808.txt">Table of n, a(n) for n = 4..10000</a> (terms 4..1000 from Alois P. Heinz)

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

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

%t 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)]];

%t a[n_] := T[n, 3];

%t Table[a[n], {n, 4, 50}] (* _Jean-François Alcover_, May 11 2019, after _Alois P. Heinz_ in A244925 *)

%Y Cf. A048809-A048816.

%Y Column k=3 of A244925.

%K nonn

%O 4,3

%A _Christian G. Bower_, Apr 15 1999