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