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

0,3

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.

Example

0, 1/2, 25/48, 1129/2160, 63251/120960, 1581371/3024000, 52185743/99792000, ... -> Pi^2/18.

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

Mathematica

Join[{0}, Numerator[Accumulate[Table[1/(i^3 Binomial[2i, i]), {i, 20}]]]] (* Harvey P. Dale, May 28 2014 *)

Prog

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

Crossrefs

Cf. A086463 (Pi^2/18), A112103 (denominator).

Sequence in context: A066852 A123204 A012508 * A012799 A120694 A012809

Adjacent sequences: A112099 A112100 A112101 * A112103 A112104 A112105

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 30 2005

Extensions

Definition corrected (and an incorrect sum deleted) by Wolfdieter Lang, Oct 07 2008

Status

approved