A112103 Denominator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).

1, 2, 48, 2160, 120960, 3024000, 99792000, 63567504000, 46230912000, 77806624896000, 4548694993920, 7155097225436160, 164567236185031680, 139059314576351769600, 139059314576351769600, 100818003067855032960000, 25002864760828048174080000

Offset

0,2

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; denom(add(1/(i^3*binomial(2*i, i)), i=1..n)) end proc:
map(f, [$0..20]); # Robert Israel, Jun 22 2023

Mathematica

Table[Sum[1/(k^3 Binomial[2k, k]), {k, n}], {n, 0, 20}]//Denominator (* Harvey P. Dale, Feb 19 2023 *)

Prog

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

Crossrefs

Cf. A086463 (Pi^2/18), A112102 (numerator).

Sequence in context: A186284 A119695 A119698 * A367254 A177317 A114714

Adjacent sequences: A112100 A112101 A112102 * A112104 A112105 A112106

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