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 A066768 Sum_{d|n} binomial(2*d-2,d-1). 1
 1, 3, 7, 23, 71, 261, 925, 3455, 12877, 48693, 184757, 705713, 2704157, 10401527, 40116677, 155120975, 601080391, 2333619351, 9075135301, 35345312513, 137846529751, 538258059199, 2104098963721, 8233431436745, 32247603683171 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA G.f.: Sum_{n>=1} x^n/sqrt(1-4*x^n). [From Paul D. Hanna, Aug 23 2011] Logarithmic derivative of A052854, the number of unordered forests on n nodes. Equals A051731 * A000984, i.e. the inverse Mobius transform of A000984. - Gary W. Adamson, Nov 09 2007 a(n) ~ 4^(n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 08 2019 MATHEMATICA Table[Sum[Binomial[2*d-2, d-1], {d, Divisors[n]}], {n, 1, 30}] (* Vaclav Kotesovec, Jun 08 2019 *) PROG (PARI) a(n)=if(n<1, 0, sumdiv(n, d, binomial(2*d-2, d-1))) (PARI) a(n)=polcoeff(sum(m=1, n, x^m/sqrt(1-4*x^m+x*O(x^n))), n) /* Paul D. Hanna */ CROSSREFS Cf. A034731, A052854. Cf. A051731, A000984. Sequence in context: A045610 A045723 A140456 * A225914 A062241 A000229 Adjacent sequences:  A066765 A066766 A066767 * A066769 A066770 A066771 KEYWORD nonn AUTHOR Vladeta Jovovic, Jan 17 2002 STATUS approved

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Last modified November 25 14:47 EST 2020. Contains 338625 sequences. (Running on oeis4.)