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A112103
Denominator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
5
1, 2, 48, 2160, 120960, 3024000, 99792000, 63567504000, 46230912000, 77806624896000, 4548694993920, 7155097225436160, 164567236185031680, 139059314576351769600, 139059314576351769600, 100818003067855032960000, 25002864760828048174080000
OFFSET
0,2
LINKS
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
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