A066768 Sum_{d|n} binomial(2*d-2,d-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

Offset: 1

Author

Vladeta Jovovic, Jan 17 2002

Keywords

• nonn

Crossrefs

Cf. A034731, A052854.

Cf. A051731, A000984.

Programs

Mathematica

Table[Sum[Binomial[2*d-2,d-1], {d, Divisors[n]}], {n,1,30}] (* Vaclav Kotesovec, Jun 08 2019 *)

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 */

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