|
%I #13 Jun 08 2019 07:25:36
%S 1,3,7,23,71,261,925,3455,12877,48693,184757,705713,2704157,10401527,
%T 40116677,155120975,601080391,2333619351,9075135301,35345312513,
%U 137846529751,538258059199,2104098963721,8233431436745,32247603683171
%N Sum_{d|n} binomial(2*d-2,d-1).
%F G.f.: Sum_{n>=1} x^n/sqrt(1-4*x^n). [From Paul D. Hanna, Aug 23 2011]
%F Logarithmic derivative of A052854, the number of unordered forests on n nodes.
%F Equals A051731 * A000984, i.e. the inverse Mobius transform of A000984. - _Gary W. Adamson_, Nov 09 2007
%F a(n) ~ 4^(n-1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jun 08 2019
%t Table[Sum[Binomial[2*d-2,d-1], {d, Divisors[n]}], {n,1,30}] (* _Vaclav Kotesovec_, Jun 08 2019 *)
%o (PARI) a(n)=if(n<1,0,sumdiv(n,d,binomial(2*d-2,d-1)))
%o (PARI) a(n)=polcoeff(sum(m=1,n,x^m/sqrt(1-4*x^m+x*O(x^n))),n) /* Paul D. Hanna */
%Y Cf. A034731, A052854.
%Y Cf. A051731, A000984.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Jan 17 2002
|
