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A295583
a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*2^d*a(n/d).
3
1, 2, 8, 24, 112, 256, 3456, 7040, 121856, 889344, 9521152, 19044352, 1485742080, 2971492352, 127715852288, 2347710726144, 26083162292224, 52166324715520, 8207231011651584, 16414462023827456, 3388603178995417088, 55218988565243363328, 646700039922421596160, 1293400079844851580928
OFFSET
1,2
COMMENTS
Suggested by Eq. (80) of (Maia and Mendez, 2008).
LINKS
M. Maia and M. Mendez, On the arithmetic product of combinatorial species, Discr. Math., 308 (2008), 5407-5427.
MAPLE
with(numtheory);
B:=(n, d)->n!/(d!*(n/d)!);
f:=proc(n) local d; global B; option remember;
if n=1 then 1
else add( B(n-1, d)*2^d*f((n-1)/d), d in divisors(n-1)); fi;
end;
[seq(f(n), n=1..40)];
CROSSREFS
Sequence in context: A150666 A150667 A150668 * A150669 A157005 A123775
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 09 2017
STATUS
approved