|
%I #29 Apr 13 2020 13:01:30
%S 1,1,1,1,1,1,6,21,56,126,252,492,1062,2667,7252,19509,49824,121019,
%T 286974,687384,1702308,4357383,11322408,29307458,74897808,189349041,
%U 477491356,1211349276,3103673406,8017385416,20780391882,53812468392,138999941172,358502419242
%N Number of 6-ary search trees on n keys.
%H Alois P. Heinz, <a href="/A019500/b019500.txt">Table of n, a(n) for n = 0..700</a>
%H J. A. Fill and R. P. Dobrow, <a href="https://people.carleton.edu/~rdobrow/Papers/NumberMary.pdf">The number of m-ary search trees on n keys</a>, Combin. Probab. Comput. 6 (1997), 435-453.
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) ~ c * d^n / n^(3/2), where d = 2.705312740243..., c = 0.3835479397... . - _Vaclav Kotesovec_, Sep 06 2014
%p A:= proc(n) option remember; if n=0 then 1 else convert(series(
%p add(x^i, i=0..4)+ x^5*A(n-1)^6, x=0,n+1), polynom) fi
%p end:
%p a:= n-> coeff(A(n), x, n):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, Aug 22 2008
%t A[n_] := A[n] = If[n==0, 1, Series[Sum[x^i, {i, 0, 4}] + x^5*A[n-1]^6, {x, 0, n+1}] // Normal]; a[n_] := Coefficient[A[n], x, n]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 19 2016, after _Alois P. Heinz_ *)
%K nonn
%O 0,7
%A James Fill (jimfill(AT)jhu.edu)
%E More terms from _Alois P. Heinz_, Aug 22 2008
|
