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A295578
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a(1)=1; thereafter, a(n+1) = Sum_{d divides n} (n!/(d!*(n/d)!))*(n/d)*a(d).
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3
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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
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OFFSET
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1,3
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COMMENTS
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Suggested by Eq. (80) of (Maia and Mendez, 2008).
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LINKS
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MAPLE
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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)];
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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