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A061160
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Numerators in expansion of Euler transform of b(n) = 1/3.
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4
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1, 1, 5, 50, 215, 646, 8711, 25475, 105925, 3091270, 11691247, 36809705, 445872155, 1364113925, 5085042010, 50975292560, 183383680088, 588817265695, 19512559194875, 62369303509475, 224877933068647, 2214198452392027, 7686538660149565, 25124342108522750
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OFFSET
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0,3
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COMMENTS
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Denominators of c(n) are 3^d(n), where d(n)=power of 3 in (3*n)!, cf. A004128.
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LINKS
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FORMULA
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Numerators of c(n), where c(n) = (1/(3*n))*Sum_{k=1..n} c(n-k)*sigma(k), n>0, c(0)=1.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, add(add(
d/3, d=numtheory[divisors](j))*b(n-j), j=1..n)/n)
end:
a:= n-> numer(b(n)):
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MATHEMATICA
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c[n_] := c[n] = If[n == 0, 1,
(1/(3n)) Sum[c[n-k] DivisorSigma[1, k], {k, 1, n}]];
a[n_] := Numerator[c[n]];
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CROSSREFS
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KEYWORD
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easy,nonn,frac
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AUTHOR
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STATUS
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approved
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