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A122698
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a(1)=a(2)=1 then a(n) = Sum_{d|n, 1<d<n} a(d)*a(n/d).
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8
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1, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,8
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LINKS
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FORMULA
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a(1) = 1, for k>=0 a(2^(k+1)) = A000108(k) and if n>1 is not a power of 2 a(n) = 0.
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MATHEMATICA
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a[1] = a[2] = 1; a[n_] := a[n] = DivisorSum[n, a[#] * a[n/#] &, 1 < # < n &]; Array[a, 100]
(* or *)
a[n_] := Module[{e = IntegerExponent[n, 2]}, If[n == 2^e, CatalanNumber[e-1], 0]]; a[1] = 1; a[n_?OddQ] = 0; Array[a, 100] (* Amiram Eldar, Sep 05 2023 *)
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PROG
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(PARI) a(n)=if(n<3, 1, sumdiv(n, d, if((d-1)*(d-n), a(d)*a(n/d), 0)))
(PARI) a(n)={my(e=valuation(n, 2)); if(n==1<<e, if(e==0, 1, binomial(2*e-2, e-1)/e), 0)} \\ Andrew Howroyd, Aug 05 2018
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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