%I #25 Apr 13 2020 13:02:36
%S 1,1,1,1,1,5,15,35,70,146,360,980,2620,6620,16276,40740,105820,280780,
%T 743700,1950756,5101470,13429110,35693650,95433290,255434106,
%U 683340050,1829832350,4913953750,13239959100,35758234300,96702404700,261768987260,709479051420
%N Number of 5-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..3)+ x^4*A(n-1)^5, 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[1 + x + x^2 + x^3 + x^4*A[n-1]^5, {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 0,6
%A James Fill (jimfill(AT)jhu.edu)
%E More terms from _Alois P. Heinz_, Aug 22 2008