A130034 Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(2)/2.

1, 8, 256, 2048, 262144, 2097152, 67108864, 536870912, 274877906944, 2199023255552, 70368744177664, 562949953421312, 72057594037927936, 576460752303423488, 18446744073709551616, 147573952589676412928

Offset

0,2

Comments

See the references and the W. Lang link under A129934.

Links

G. C. Greubel, Table of n, a(n) for n = 0..665

Formula

a(n) = denom(sum((((2*j)!/(j!^2))^2)*(1/2^(5*j)),j=0..n)), n>=0.

Mathematica

Denominator[Table[Sum[(((2*k)!/(k!^2))^2)*(1/2^(5*k)), {k, 0, n}], {n, 0, 50}]] (* G. C. Greubel, Aug 17 2018 *)

Prog

(PARI) for(n=0, 50, print1(denominator(sum(k=0, n, (((2*k)!/(k!^2))^2)*(1/2^(5*k)))), ", ")) \\ G. C. Greubel, Aug 17 2018

Crossrefs

Sequence in context: A317511 A300176 A291850 * A128787 A013824 A010044

Adjacent sequences: A130031 A130032 A130033 * A130035 A130036 A130037

Keyword

nonn,frac,easy

Author

Wolfdieter Lang Jun 01 2007

Status

approved