A167912 a(n) = (1/(3^n)^2) * Sum_{k=0..(3^n-1)} binomial(2k,k).

1, 217, 913083596083, 18744974860247264575032720770000376335095039

Offset: 1

Author

Alexander Adamchuk, Nov 15 2009

Keywords

• nonn

Comments

Note that a(n) mod 27 = a(n) mod 9 = a(n) mod 3 = 1.

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

Links

• Eric Weisstein's World of Mathematics, Central Binomial Coefficient.
• Eric Weisstein's World of Mathematics, Binomial Sums.

Crossrefs

Cf. A006134, A083096, A066796, A083097, A081601, A010060, A122485.

Programs

Maple

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

Mathematica

Table[(1/3^n)^2 * Sum[Binomial[2 k, k], {k, 0, 3^n - 1}], {n, 1, 5}] (* G. C. Greubel, Jul 01 2016 *)

Extensions

a(4) from Emeric Deutsch, Nov 22 2009