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A035054 Number of forests of identical trees. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 19 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A005195.

Sequence in context: A110199 A222736 A053656 * A099537 A109525 A243330

Adjacent sequences:  A035051 A035052 A035053 * A035055 A035056 A035057

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1998.

STATUS

approved

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Last modified January 18 11:28 EST 2019. Contains 319271 sequences. (Running on oeis4.)