A038000 Number of forests of rooted trees where n dollars are spent and an n-node tree costs 2n-1 dollars.

1, 1, 2, 2, 4, 5, 9, 11, 21, 28, 50, 68, 123, 173, 310, 441, 789, 1147, 2044, 2999, 5351, 7938, 14143, 21138, 37686, 56729, 101144, 153085, 273077, 415407, 741301, 1132373, 2021831, 3100128, 5537782, 8519076, 15225373, 23491413, 42003748, 64979069, 116239502

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Formula

EULER transform of {c(x)} where {c(x)} has g.f. B(x^2)/x = x+x^3+2*x^5+4*x^7+9*x^9+... and B(x) = x+x^2+2*x^3+4*x^4+9*x^5+... is g.f. for A000081.

Maple

with(numtheory):
b:= proc(n) option remember; local d, j; `if`(n<=1, n,
      (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
    end:
c:= proc(n) local r; `if`(irem(n, 2, 'r')=0, 0, b(r+1)) end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(add(d*c(d), d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 16 2013

Mathematica

b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}])/(n-1)]; c[n_] := If[Mod[n, 2]==0, 0, b[n/2 // Ceiling]];  a[n_] := a[n] = If[n==0, 1, Sum[Sum[d*c[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *)

Crossrefs

Sequence in context: A099574 A144118 A187069 * A089935 A204856 A323531

Adjacent sequences: A037997 A037998 A037999 * A038001 A038002 A038003

Keyword

nonn,easy

Author

Christian G. Bower

Status

approved