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

1,1

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.

Links

Table of n, a(n) for n=1..16.

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A247014 A085055 A075070 * A009110 A225170 A134958

Adjacent sequences: A144934 A144935 A144936 * A144938 A144939 A144940

Keyword

nonn

Author

Washington Bomfim, Sep 25 2008

Status

approved