OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Jan 17 2002
STATUS
approved