A134805 Denominator of Sum_{i=1..n} 1/(i^2*binomial(2*i,i)).

1, 2, 24, 360, 2016, 16800, 237600, 151351200, 605404800, 30875644800, 53330659200, 6453009763200, 11416863427200, 1929449919196800, 1929449919196800, 93256746094512000, 680225677395264000, 196585220767231296000, 93119315100267456000, 1243794691794272409792000

Offset

0,2

Comments

For this sum times 2/3 see A130549/A130550 with offset 1.

Links

Table of n, a(n) for n=0..19.

C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.

Formula

Sum_{i >= 1} 1/(i^2*binomial(2*i, i)) = Pi^2/18.

Example

0, 1/2, 13/24, 197/360, 1105/2016, 9211/16800, 130277/237600, 82987349/151351200, ...

Maple

seq(denom(add(1/(k^2*binomial(2*k, k)), k = 1 .. n)), n = 0 .. 19); # Peter Bala, Mar 03 2015

Mathematica

Join[{1}, Denominator[Accumulate[Table[1/(n^2 Binomial[2n, n]), {n, 20}]]]] (* Harvey P. Dale, Jun 07 2021 *)

Prog

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

Crossrefs

For numerators see A130549, n>=1.

Sequence in context: A220317 A220340 A366003 * A119702 A126804 A344057

Adjacent sequences: A134802 A134803 A134804 * A134806 A134807 A134808

Keyword

nonn,frac

Author

Wolfdieter Lang and N. J. A. Sloane, Oct 13 2008

Status

approved