A112102 - OEIS

%I #20 Jan 05 2025 19:51:38

%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="https://web.archive.org/web/2024*/https://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