A274654 Denominators of coefficients of z^n/n! for the expansion of Fricke's hypergeometric function F_1(1/2,1/2;z).

1, 2, 32, 128, 4096, 16384, 131072, 524288, 33554432, 134217728, 1073741824, 4294967296, 68719476736, 274877906944, 2199023255552, 8796093022208, 1125899906842624, 4503599627370496, 36028797018963968, 144115188075855872, 2305843009213693952

Offset

0,2

Comments

The numerators are given in A274653, where one finds the definition of Fricke's F1(a,b;z) by a recurrence and references.

References

See A274653.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = denominator(r(n)), with the rationals (in lowest terms) defined by the recurrence

r(n) = ((2*n-1)^2/(4*n))*r(n-1) + 2*c(n)/(n*(2*n-1)), n >= 1, r(0) = 0, with c(n) = ((2*n)!)^2 / (n!^3*2^(4*n)).

Example

See A274653.

Crossrefs

Cf. A274653.

Sequence in context: A226395 A257965 A191997 * A112850 A123105 A123287

Adjacent sequences: A274651 A274652 A274653 * A274655 A274656 A274657

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 07 2016

Status

approved