A112102 Numerator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
0, 1, 25, 1129, 63251, 1581371, 52185743, 33242372291, 24176277773, 40688677687159, 2378722720177, 3741730846458901, 86059809503772983, 72720539036773885963, 72720539038037143387, 52722390802769505531767, 13075152919096992777263341
Offset: 0
Examples
0, 1/2, 25/48, 1129/2160, 63251/120960, 1581371/3024000, 52185743/99792000, ... -> Pi^2/18.
Links
- Robert Israel, Table of n, a(n) for n = 0..576
- C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.
Programs
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Maple
f:= proc(n) local i; numer(add(1/(i^3*binomial(2*i,i)),i=1..n)) end proc: map(f, [$0..20]); # Robert Israel, Jun 22 2023
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Mathematica
Join[{0},Numerator[Accumulate[Table[1/(i^3 Binomial[2i,i]),{i,20}]]]] (* Harvey P. Dale, May 28 2014 *) -
PARI
a(n) = numerator(sum(i=1, n, 1/(i^3*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016
Extensions
Definition corrected (and an incorrect sum deleted) by Wolfdieter Lang, Oct 07 2008