|
%I #18 Jun 06 2021 09:02:18
%S 1,217,913083596083,18744974860247264575032720770000376335095039
%N a(n) = (1/(3^n)^2) * Sum_{k=0..(3^n-1)} binomial(2k,k).
%C Note that a(n) mod 27 = a(n) mod 9 = a(n) mod 3 = 1.
%C The Maple program yields the first seven terms; easily adjustable for obtaining more terms. However, a(4) has 44 digits, a(5) has 140 digits, a(6) has 432 digits and a(7) has 1308 digits. - _Emeric Deutsch_, Nov 22 2009
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CentralBinomialCoefficient.html">Central Binomial Coefficient</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>.
%p a := proc (n) options operator, arrow: (sum(binomial(2*k, k), k = 0 .. 3^n-1))/3^(2*n) end proc: seq(a(n), n = 1 .. 7); # _Emeric Deutsch_, Nov 22 2009
%t Table[(1/3^n)^2 * Sum[Binomial[2 k, k], {k, 0, 3^n - 1}], {n, 1, 5}] (* _G. C. Greubel_, Jul 01 2016 *)
%Y Cf. A006134, A083096, A066796, A083097, A081601, A010060, A122485.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Nov 15 2009
%E a(4) from _Emeric Deutsch_, Nov 22 2009
|
