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a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*a(d).
4

%I #16 Dec 11 2017 05:05:06

%S 1,1,2,3,10,11,192,193,3554,23715,190036,190037,20813718,20813719,

%T 1690001240,23484574041,182792522842,182792522843,50810028382044,

%U 50810028382045,18982767399108446,346748732389572447,3022335531740638048,3022335531740638049,1128891498261322308450,11900565139463395908451

%N a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*a(d).

%C It is possible that A092986 (Maia and Mendez, 2008, Table 1) is an erroneous version of this sequence.

%H Seiichi Manyama, <a href="/A295577/b295577.txt">Table of n, a(n) for n = 1..454</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. See Table 1.

%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)!))*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/#)!))*f@#) & /@ Divisors@ m]]; f[1] = 1; Array[f, 26] (* _Robert G. Wilson v_, Dec 10 2017 *)

%Y Cf. A092986, A295578, A295583.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Dec 09 2017