A295583 a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*2^d*a(n/d).

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

Seiichi Manyama, Table of n, a(n) for n = 1..452

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

Cf. A295577, A295578.

Sequence in context: A150666 A150667 A150668 * A150669 A157005 A123775

Adjacent sequences: A295580 A295581 A295582 * A295584 A295585 A295586

Keyword

nonn

Author

N. J. A. Sloane, Dec 09 2017

Status

approved