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A144979
Number of hyperforests on n unlabeled nodes, assuming that each edge contains at least two nodes, with all components of prime orders.
0
0, 1, 2, 3, 11, 15, 70, 92, 166, 351, 5061, 5782, 60736, 73183, 135152, 303426, 8507114, 9468630, 119603007, 140712654, 262160102, 593434948, 21042972101, 23146479248, 44736887989, 96738104613, 122459045525
OFFSET
1,3
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.
FORMULA
a(n) = Sum of prod_{k=1..n} C(A035053(k)+c_k-1,c_k}) over the partitions of n having all parts k prime, c_1 + 2c_2 + ... + nc_n; c_1, c_2, ..., c_n >= 0.
EXAMPLE
a(5) = 11 since the only options are 9 hypertrees of order 5, or the two hyperforests composed by components of order 3 and 2.
CROSSREFS
Cf. A035053 (hypertrees), A000040 (prime numbers).
Sequence in context: A295128 A360520 A066687 * A194558 A076514 A071012
KEYWORD
nonn
AUTHOR
Washington Bomfim, Sep 28 2008
STATUS
approved