The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A215852 Number of simple labeled graphs on n nodes with exactly 2 connected components that are trees or cycles. 3
 1, 3, 19, 135, 1267, 15029, 218627, 3783582, 75956664, 1734309929, 44357222772, 1255715827483, 38971877812380, 1315634598619830, 47994245894462576, 1881406032047006812, 78870928008704884848, 3520953336130828001295, 166762291211479030734580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..145 FORMULA a(n) ~ c * n^(n-2), where c = 0.511564031298... . - Vaclav Kotesovec, Sep 07 2014 EXAMPLE a(3) = 3: .1 2.  .1-2.  .1 2. .|. .  . . .  . / . .3...  .3...  .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, 2): seq(a(n), n=2..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}]]]; Table[T[n, 2], {n, 2, 50}] (* Indranil Ghosh, Aug 07 2017, after Maple *) PROG (Python) from sympy.core.cache import cacheit from sympy import binomial, factorial as f @cacheit def T(n, k): return 0 if k<0 or k>n else 1 if n==0 else sum([binomial(n - 1, i)*T(n - 1 - i, k - 1)*(1 if i<2 else f(i)/2 + (i + 1)**(i - 1)) for i in range(n - k + 1)]) def a(n): return T(n , 2) print map(a, range(2, 51)) # Indranil Ghosh, Aug 07 2017, after maple code CROSSREFS Column k=2 of A215861. The unlabeled version is A215982. Sequence in context: A091346 A305550 A035086 * A105797 A278189 A221297 Adjacent sequences:  A215849 A215850 A215851 * A215853 A215854 A215855 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 25 2012 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 28 23:08 EST 2020. Contains 332351 sequences. (Running on oeis4.)