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A295578
a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*(n/d)*a(d).
3
1, 1, 3, 6, 22, 27, 573, 580, 14028, 104757, 845647, 845658, 120596070, 120596083, 10092478017, 157205844432, 1332037102048, 1332037102065, 395631664423683, 395631664423702, 170313938200001322, 3110070531413441343, 26922450918793025365, 26922450918793025388, 10816813121713202599812
OFFSET
1,3
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);
f:=proc(n) local d; option remember;
if n=1 then 1
else add( ((n-1)!/(d!*((n-1)/d)!))*((n-1)/d)*f(d), d in divisors(n-1)); fi;
end;
[seq(f(n), n=1..40)];
MATHEMATICA
f[n_] := Block[{m = n - 1}, Plus @@ Flatten[((m!/(#!*(m/#)!)) (m/#)*f@#) & /@ Divisors@m]]; f[1] = 1; Array[f, 25] (* Robert G. Wilson v, Dec 10 2017 *)
CROSSREFS
Sequence in context: A236056 A347616 A280116 * A054297 A325158 A079514
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 09 2017
STATUS
approved