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A213674 Number of rooted trees with n nodes, where cycles are allowed instead of subtrees. 3
0, 1, 1, 3, 6, 13, 29, 71, 176, 454, 1188, 3168, 8542, 23319, 64201, 178249, 498241, 1401344, 3962353, 11257882, 32122442, 92011118, 264474749, 762620137, 2205415254, 6394813039, 18587795338, 54151405093, 158088694125, 462420145673, 1355063144072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 3.0842695283018951389734653060490863..., c = 0.46707331868314508788370370390913... . - Vaclav Kotesovec, Sep 07 2014

EXAMPLE

: o : o :   o     o   o :   o     o     o     o     o   o :

:   : | :  / \   / \  | :  / \    |     |    / \   /|\  | :

:   : o : o---o o   o o : o   o   o     o   o   o o o o o :

:   :   :             | :  \ /   / \   / \  |           | :

:   :   :             o :   o   o---o o   o o           o :

:   :   :               :                               | :

:n=1.n=2. n=3           . n=4                           o :

...........................................................

MAPLE

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

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

    end:

a:= n-> b(n-1, n-1) +`if`(n>2, 1, 0):

seq(a(n), n=0..40);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[a[i]+j-1, j]*b[n-i*j, i-1], {j, 0, n/i}]] // FullSimplify] ; a[n_] := b[n-1, n-1] + If[n>2, 1, 0]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Feb 05 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A000081, A213682, A213683.

Sequence in context: A018909 A093128 A005313 * A108639 A327795 A087218

Adjacent sequences:  A213671 A213672 A213673 * A213675 A213676 A213677

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified March 8 00:38 EST 2021. Contains 341934 sequences. (Running on oeis4.)