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%I #18 Jun 23 2023 02:30:59
%S 0,1,25,1129,63251,1581371,52185743,33242372291,24176277773,
%T 40688677687159,2378722720177,3741730846458901,86059809503772983,
%U 72720539036773885963,72720539038037143387,52722390802769505531767,13075152919096992777263341
%N Numerator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
%H Robert Israel, <a href="/A112102/b112102.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; numer(add(1/(i^3*binomial(2*i,i)),i=1..n)) end proc:
%p map(f, [$0..20]); # _Robert Israel_, Jun 22 2023
%t Join[{0},Numerator[Accumulate[Table[1/(i^3 Binomial[2i,i]),{i,20}]]]] (* _Harvey P. Dale_, May 28 2014 *)
%o (PARI) a(n) = numerator(sum(i=1, n, 1/(i^3*binomial(2*i, i)))); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A086463 (Pi^2/18), A112103 (denominator).
%K nonn,frac
%O 0,3
%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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