A144935 Number of hyperforests with n labeled vertices when edges of size 1 are allowed (with no two equal edges), without isolated nodes nor isolated loops.

0, 4, 32, 512, 11232, 323648, 11616768, 500984576, 25275854848, 1461945274368, 95418154739712, 6939291871629312, 556552095965593600, 48807623034247200768, 4646562962112939622400, 477275845583045903777792

Offset

1,2

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) = Sum of n!prod_{k=1}^n\{ frac{ A134958(k)^{c_k} }{ k!^{c_k} c_k! } } over all the partitions of n with parts k > 1, c_1 + 2c_2 + ... + nc_n; c_1, c_2, ..., c_n >= 0.

Example

a(5) = 11232 since the partitions of 5 with parts > 1 are [5] and [3,2]. The partition [5] corresponds to 9952 hypergraphs and [3,2] corresponds to 5!4/2!32/3! = 1280.

Crossrefs

Cf. A134958(hypertrees), A134956(hyperforests).

Sequence in context: A192487 A093581 A102557 * A153511 A140179 A118990

Adjacent sequences: A144932 A144933 A144934 * A144936 A144937 A144938

Keyword

nonn

Author

Washington Bomfim, Sep 25 2008

Status

approved