A035054 Number of forests of identical trees.

1, 1, 2, 2, 4, 4, 9, 12, 27, 49, 111, 236, 562, 1302, 3172, 7746, 19347, 48630, 123923, 317956, 823178, 2144518, 5623993, 14828075, 39300482, 104636894, 279794753, 751065509, 2023446206, 5469566586, 14830879661, 40330829031, 109972429568, 300628862717

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..750

N. J. A. Sloane, Transforms

Formula

Inverse Moebius transform of A000055.

a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856519949747148..., c = A086308 = 0.53494960614230701455... . - Vaclav Kotesovec, Aug 25 2014

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n<=1, n,
      (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
    end:
g:= proc(n) option remember; local k; `if`(n=0, 1, b(n)-
      (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2)
    end:
a:= n-> `if`(n=0, 1, add(g(d), d=divisors(n))):
seq(a(n), n=0..35);  # Alois P. Heinz, May 18 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)]; g[n_] := g[n] = If[n==0, 1, b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[Mod[n, 2]==0, b[n/2], 0])/2]; a[n_] := If[n==0, 1, Sum[ g[d], {d, Divisors[n]}]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *)

Crossrefs

Cf. A005195.

Sequence in context: A222736 A053656 A364752 * A099537 A109525 A243330

Adjacent sequences: A035051 A035052 A035053 * A035055 A035056 A035057

Keyword

nonn

Author

Christian G. Bower, Oct 15 1998.

Status

approved