A144937 Number of hyperforests with n labeled vertices when edges of size 1 are allowed (with no two equal edges), with at least one component of order 1.

2, 4, 32, 368, 6752, 171648, 5638656, 227787008, 10932927488, 608031869952, 38451260291072, 2724757330591744, 213848122843791360, 18412354032091807744, 1725472542353497456640, 174827224579118545174528

Offset: 1

Author

Washington Bomfim, Sep 25 2008

Keywords

• nonn

Examples

			For n=2 we do not have an hypertree of order 2. The possibilities are one forest, two hyperforests composed by one loop plus one tree and one hyperforest composed by two loops. So a(2)=4.
		

References

• D. E. Knuth: The Art of Computer Programming, Volume 4, Generating All Combinations and Partitions Fascicle 3, Section 7.2.1.4. Generating all partitions. Page 38, Algorithm H.

Crossrefs

Cf. A134956(hyperforests), A144935(hyperforests without components of order 1).

Formula

a(n) = A134956(n) - A144935(n).