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%I #21 Jun 23 2023 02:31:14
%S 1,2,48,2160,120960,3024000,99792000,63567504000,46230912000,
%T 77806624896000,4548694993920,7155097225436160,164567236185031680,
%U 139059314576351769600,139059314576351769600,100818003067855032960000,25002864760828048174080000
%N Denominator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
%H Robert Israel, <a href="/A112103/b112103.txt">Table of n, a(n) for n = 0..576</a>
%H C. Elsner, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-5.pdf">On recurrence formulas for sums involving binomial coefficients</a>, Fib. Q., 43,1 (2005), 31-45.
%e 0, 1/2, 25/48, 1129/2160, 63251/120960, 1581371/3024000, 52185743/99792000, ... -> Pi^2/18.
%p f:= proc(n) local i; denom(add(1/(i^3*binomial(2*i,i)),i=1..n)) end proc:
%p map(f, [$0..20]); # _Robert Israel_, Jun 22 2023
%t Table[Sum[1/(k^3 Binomial[2k,k]),{k,n}],{n,0,20}]//Denominator (* _Harvey P. Dale_, Feb 19 2023 *)
%o (PARI) a(n) = denominator(sum(i=1, n, 1/(i^3*binomial(2*i, i)))); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A086463 (Pi^2/18), A112102 (numerator).
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 30 2005
%E Definition corrected (and an incorrect sum deleted) by _Wolfdieter Lang_, Oct 07 2008
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