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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

Table of n, a(n) for n=1..25.

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.)