A112094 - OEIS

A112094

Denominator of 3*Sum_{i=1..n} 1/(i^2*C(2*i,i)).

1, 2, 8, 120, 672, 5600, 79200, 50450400, 201801600, 10291881600, 17776886400, 2151003254400, 3805621142400, 643149973065600, 643149973065600, 31085582031504000, 226741892465088000, 65528406922410432000, 31039771700089152000, 414598230598090803264000, 16583929223923632130560

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.

FORMULA

3*Sum_{i >= 1} 1/(i^2*C(2*i, i)) = zeta(2) = Pi^2/6.

EXAMPLE

0, 3/2, 13/8, 197/120, 1105/672, 9211/5600, 130277/79200, 82987349/50450400, ... -> Pi^2/6.

PROG

(PARI) a(n) = denominator(3*sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016