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%I #18 Dec 10 2017 17:04:55
%S 1,1,3,6,22,27,573,580,14028,104757,845647,845658,120596070,120596083,
%T 10092478017,157205844432,1332037102048,1332037102065,395631664423683,
%U 395631664423702,170313938200001322,3110070531413441343,26922450918793025365,26922450918793025388,10816813121713202599812
%N a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*(n/d)*a(d).
%C Suggested by Eq. (80) of (Maia and Mendez, 2008).
%H Seiichi Manyama, <a href="/A295578/b295578.txt">Table of n, a(n) for n = 1..453</a>
%H M. Maia and M. Mendez, <a href="https://doi.org/10.1016/j.disc.2007.09.062">On the arithmetic product of combinatorial species</a>, Discr. Math., 308 (2008), 5407-5427.
%p with(numtheory);
%p f:=proc(n) local d; option remember;
%p if n=1 then 1
%p else add( ((n-1)!/(d!*((n-1)/d)!))*((n-1)/d)*f(d), d in divisors(n-1)); fi;
%p end;
%p [seq(f(n),n=1..40)];
%t 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 *)
%Y Cf. A295577, A295583.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Dec 09 2017
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