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A215853 Number of simple labeled graphs on n nodes with exactly 3 connected components that are trees or cycles. 3
1, 6, 55, 540, 6412, 90734, 1515097, 29368155, 649910349, 16178495157, 447436384356, 13607804913248, 451277483034618, 16204761730619392, 626327433705523558, 25924177756443661632, 1144012780063556028591, 53615833082093775740400, 2659498185704802765924159 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..145

FORMULA

a(n) ~ c * n^(n-2), where c = 0.130848879059... . - Vaclav Kotesovec, Sep 07 2014

EXAMPLE

a(4) = 6:

.1-2.  .1 2.  .1 2.  .1 2.  .1 2.  .1 2.

.   .  .  |.  .   .  .|  .  . \ .  . / .

.4 3.  .4 3.  .4-3.  .4 3.  .4 3.  .4 3.

MAPLE

T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,

      `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*

      `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))

    end:

a:= n-> T(n, 3):

seq(a(n), n=3..25);

MATHEMATICA

T[n_, k_] := T[n, k] = If[k<0 || k>n, 0, If[n == 0, 1, Sum[Binomial[n-1, i]*T[n-1-i, k-1]*If[i<2, 1, i!/2 + (i+1)^(i-1)], {i, 0, n-k}]]];

a[n_] := T[n, 3];

Table[a[n], {n, 3, 25}] (* Jean-Fran├žois Alcover, Apr 01 2017, translated from Maple *)

CROSSREFS

Column k=3 of A215861.

The unlabeled version is A215983.

Sequence in context: A198855 A318592 A253475 * A110431 A121661 A118836

Adjacent sequences:  A215850 A215851 A215852 * A215854 A215855 A215856

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 25 2012

STATUS

approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)