A215763 Number of undirected labeled graphs on n nodes with exactly 3 cycle graphs as connected components.

1, 6, 25, 120, 742, 5446, 45559, 427275, 4437279, 50532669, 626068404, 8382651732, 120614527728, 1855938746160, 30411098170560, 528670269132480, 9718179216603840, 188342519176964160, 3838144417230700800, 82046606738914540800, 1835772107381126208000

Offset: 3

Author

Alois P. Heinz, Aug 23 2012

Keywords

• nonn

Examples

			a(4) = 6:  .1.2o  .1-2.  o1.2.  o1.2o  o1.2.  .1.2o
.          .|...  .....  ...|.  .....  ../..  ..\..
.          .3.4o  o3.4o  o3.4.  .3-4.  .3.4o  o3.4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..175

Crossrefs

Column k=3 of A215771.

Programs

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)*ceil(i!/2), i=0..n-k)))
    end:
a:= n-> T(n, 3):
seq (a(n), n=3..25);