login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174145 Number of rooted forests with n nodes in which each component contains at least two nodes. 4
1, 0, 1, 2, 5, 11, 28, 67, 171, 433, 1123, 2924, 7720, 20487, 54838, 147570, 399466, 1086312, 2967517, 8137552, 22395604, 61833349, 171227674, 475442129, 1323449661, 3692461865, 10324097819, 28923331940, 81179488039, 228240293289, 642744665401, 1812762839702 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums of A174135.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.8603881121111431... . - Vaclav Kotesovec, Sep 10 2014

In the asymptotics above the constant c = A187770 * (A051491 - 1). - Vladimir Reshetnikov, Aug 12 2016

a(n) = A000081(n+1) - A000081(n). - Vladimir Reshetnikov, Nov 06 2015

MAPLE

with(numtheory):

t:= proc(n) option remember; local d, j; `if`(n<=1, n,

      (add(add(d*t(d), d=divisors(j))*t(n-j), j=1..n-1))/(n-1))

    end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0,

      add(b(n-i*j, i-1)*binomial(t(i)+j-1, j), j=0..n/i)))

    end:

a:= n-> b(n, n):

seq(a(n), n=0..32);  # Alois P. Heinz, May 17 2013

MATHEMATICA

t[n_] := t[n] = If[n <= 1, n, Sum[Sum[d*t[d], {d, Divisors[j]}]*t[n-j], {j, 1, n-1}]/(n-1)]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, Sum[b[n-i*j, i-1]*Binomial[t[i]+j-1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n] // FullSimplify, {n, 0, 32}] (* Jean-Fran├žois Alcover, Mar 19 2014, after Alois P. Heinz *)

t[1] = 1; t[n_] := t[n] = Sum[k t[k] t[n - k m]/(n-1), {k, n-1}, {m, (n-1)/k}]; a[n_] := t[n+1] - t[n]; Table[a[n], {n, 0, 32}] (* Vladimir Reshetnikov, Aug 12 2016 *)

CROSSREFS

Cf. A000081, A051491, A187770, A255170.

Sequence in context: A027087 A055227 A257790 * A124016 A121398 A000625

Adjacent sequences:  A174142 A174143 A174144 * A174146 A174147 A174148

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 26 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 14:12 EDT 2018. Contains 316321 sequences. (Running on oeis4.)