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A097438
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a(n) = Sum_{k|n} a(k) a(n-k) for n >= 2, a(0)=0, a(1)=1.
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1
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0, 1, 1, 1, 2, 2, 5, 5, 14, 19, 37, 37, 146, 146, 317, 537, 1342, 1342, 4312, 4312, 13751, 19648, 34768, 34768, 178350, 205852, 405518, 665796, 1626743, 1626743, 6019892, 6019892, 19591134, 26897442, 48289540, 68463039, 270214317, 270214317
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OFFSET
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0,5
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COMMENTS
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If k in the sum in the definition is taken only over the proper divisors of n, the sequence is the same.
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LINKS
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EXAMPLE
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a(8) = a(1)*a(7) + a(2)*a(6) + a(4)*a(4) + a(8)*a(0) = 5 + 5 + 4 + 0 = 14.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, n, add(
a(d)*a(n-d), d=numtheory[divisors](n) minus {n}))
end:
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[n_] := a[n] = Block[{d = Drop[ Divisors[n], -1]}, Plus @@ Flatten[(a /@ d)*(a /@ (n - d))]]; Table[ a[n], {n, 0, 38}] (* Robert G. Wilson v, Aug 23 2004 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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