A130036 Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(3)/2.

1, 16, 1024, 16384, 4194304, 67108864, 4294967296, 68719476736, 70368744177664, 1125899906842624, 72057594037927936, 1152921504606846976, 295147905179352825856, 4722366482869645213696, 302231454903657293676544

Offset

0,2

Comments

See the references and the W. Lang link under A130035.

Also denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and 1/2. For the numerators and the formula see A130037. Proof of the coincidence: The prefactor of each term of the sum (first formula in A130037) is binomial(2*n,n)^2, a natural number and 3 will never divide the even denominators.

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = denom(sum((((2*j)!/(j!^2))^2)*(1/2^(6*j)),j=0..n)), n>=0.

Crossrefs

Sequence in context: A197104 A358051 A067490 * A013735 A180376 A162008

Adjacent sequences: A130033 A130034 A130035 * A130037 A130038 A130039

Keyword

nonn,frac,easy

Author

Wolfdieter Lang Jun 01 2007

Status

approved