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A247007
Number of permutations on [n] admitting a ninth root.
3
1, 1, 2, 4, 16, 80, 400, 2800, 22400, 179200, 1792000, 19712000, 216832000, 2818816000, 39463424000, 552487936000, 8839806976000, 150276718592000, 2554704216064000, 48539380105216000, 970787602104320000, 19415752042086400000, 427146544925900800000, 9824370533295718400000, 225960522265801523200000, 5649013056645038080000000, 146874339472770990080000000, 3818732827816549381939200000
OFFSET
0,3
COMMENTS
Differs from A102736 first at n=27.
LINKS
H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, Theorem 4.8.2.
MAPLE
with(combinat): with(numtheory): with(padic):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
`if`(irem(j, mul(p^ordp(9, p), p=factorset(i)))=0, (i-1)!^j*
multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..27);
CROSSREFS
Column k=9 of A247005.
Sequence in context: A340900 A347631 A102736 * A103619 A027436 A025225
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 09 2014
STATUS
approved