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A237670
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Inverse Moebius transform of Catalan numbers.
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1
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1, 3, 6, 17, 43, 140, 430, 1447, 4868, 16841, 58787, 208166, 742901, 2674872, 9694893, 35359117, 129644791, 477643702, 1767263191, 6564137275, 24466267455, 91482622429, 343059613651, 1289904356920, 4861946401495, 18367353815055, 69533550920872
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{d|n} binomial(2*d,d)/(d+1).
G.f.: Sum_{k>=1} (1-2*x^k-sqrt(1-4*x^k))/(2*x^k).
L.g.f.: -log(Product_{k>=1} (1 - x^k)^(binomial(2*k,k)/(k*(k+1)))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 20 2018
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MATHEMATICA
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Table[Sum[Binomial[2 d, d]/(d + 1), {d, Divisors[n]}], {n, 1, 100}]
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PROG
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(Maxima) a(n) := lsum(binomial(2*d, d)/(d+1), d, listify(divisors(n)));
makelist(a(n), n, 1, 40);
(Magma) [&+[Binomial(2*d, d)/(d+1): d in Divisors(n)]: n in [1..40]]; // Bruno Berselli, Feb 11 2014
(PARI) a(n) = sumdiv(n, d, binomial(2*d, d)/(d+1)); \\ Michel Marcus, May 20 2018
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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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