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%I #24 Aug 20 2022 12:13:21
%S 2,8,22,78,254,952,3434,12948,48642,185016,705434,2705178,10400602,
%T 40120040,155117794,601093338,2333606222,9075184872,35345263802,
%U 137846713906,538257877894,2104099669160,8233430727602,32247606401148
%N a(n) = Sum_{d dividing n} binomial(2d,d).
%H Seiichi Manyama, <a href="/A072929/b072929.txt">Table of n, a(n) for n = 1..1664</a>
%F G.f.: Sum_{k>=1} C(2k, k)*x^k/(1-x^k). - _Benoit Cloitre_, Apr 21 2003
%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(binomial(2*k,k)/k)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 20 2018
%F a(n) ~ 4^n / sqrt(Pi*n). - _Vaclav Kotesovec_, May 21 2018
%F a(n) = Sum_{k=1..n} C(2*gcd(n,k),gcd(n,k))/phi(n/gcd(n,k)) = Sum_{k=1..n} C(2*n/gcd(n,k),n/gcd(n,k))/phi(n/gcd(n,k)) where phi = A000010. - _Richard L. Ollerton_, May 19 2021
%t Table[Total[Binomial[2#,#]&/@Divisors[n]],{n,30}] (* _Harvey P. Dale_, Aug 20 2022 *)
%o (PARI) a(n)=sumdiv(n,d,binomial(2*d,d))
%Y Cf. A000984.
%Y Cf. A000010.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Aug 13 2002
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