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A167912 a(n) = (1/(3^n)^2) * Sum_{k=0..(3^n-1)} binomial(2k,k). 1
1, 217, 913083596083, 18744974860247264575032720770000376335095039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..4.

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

Eric Weisstein's World of Mathematics, Binomial Sums.

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 *)

CROSSREFS

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

Sequence in context: A100794 A048258 A013541 * A038662 A121379 A171404

Adjacent sequences:  A167909 A167910 A167911 * A167913 A167914 A167915

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Nov 15 2009

EXTENSIONS

a(4) from Emeric Deutsch, Nov 22 2009

STATUS

approved

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Last modified January 28 05:02 EST 2022. Contains 350654 sequences. (Running on oeis4.)