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

Author

Washington Bomfim, Sep 25 2008

Keywords

• nonn

Examples

			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.
		

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. A134958(hypertrees), A134956(hyperforests).

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.