%I #21 Apr 13 2020 13:03:45
%S 1,1,1,1,1,1,1,7,28,84,210,462,924,1758,3444,7602,19278,52458,142044,
%T 368130,905136,2130198,4895919,11280885,26685540,65491062,165584034,
%U 423910572,1080774261,2717940687,6731334225,16494155097,40308269022
%N Number of 7-ary search trees on n keys.
%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>
%p A:= proc(n) option remember; if n=0 then 1 else convert(series(
%p add(x^i, i=0..5)+ x^6*A(n-1)^7, 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, 5}] + x^6*A[n-1]^7, {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 0,8
%A James Fill (jimfill(AT)jhu.edu)
%E More terms from _Alois P. Heinz_, Aug 22 2008