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

1,2

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: A302180 A045723 A140456 * A225914 A062241 A000229

Adjacent sequences: A066765 A066766 A066767 * A066769 A066770 A066771

Keyword

nonn

Author

Vladeta Jovovic, Jan 17 2002

Status

approved