A019499 Number of 5-ary search trees on n keys.

1, 1, 1, 1, 1, 5, 15, 35, 70, 146, 360, 980, 2620, 6620, 16276, 40740, 105820, 280780, 743700, 1950756, 5101470, 13429110, 35693650, 95433290, 255434106, 683340050, 1829832350, 4913953750, 13239959100, 35758234300, 96702404700, 261768987260, 709479051420

Offset

0,6

Links

Table of n, a(n) for n=0..32.

J. A. Fill and R. P. Dobrow, The number of m-ary search trees on n keys, Combin. Probab. Comput. 6 (1997), 435-453.

Index entries for sequences related to rooted trees

Maple

A:= proc(n) option remember; if n=0 then 1 else convert(series(
      add(x^i, i=0..3)+ x^4*A(n-1)^5, x=0, n+1), polynom) fi
    end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=0..40);  # Alois P. Heinz, Aug 22 2008

Mathematica

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 *)

Crossrefs

Sequence in context: A195761 A100355 A048032 * A229885 A363618 A363608

Adjacent sequences: A019496 A019497 A019498 * A019500 A019501 A019502

Keyword

nonn

Author

James Fill (jimfill(AT)jhu.edu)

Extensions

More terms from Alois P. Heinz, Aug 22 2008

Status

approved