A255932 a(n) is the denominator of Gamma(n+1/2)^2/(2*n*Pi), the value of an integral with sinh in the denominator.

8, 64, 128, 2048, 2048, 16384, 32768, 1048576, 524288, 4194304, 8388608, 134217728, 134217728, 1073741824, 2147483648, 137438953472, 34359738368, 274877906944, 549755813888, 8796093022208, 8796093022208, 70368744177664, 140737488355328

Offset

1,1

Comments

Conjecture: a(n) <= 2^(3*n). - Vaclav Kotesovec, Mar 11 2015

Links

Table of n, a(n) for n=1..23.

MathOverflow, An identity involving an infinite integral with a sinh in the denominator

Formula

The n-th fraction also equals the n-th coefficient in the expansion of 2F1(1/2,1/2; 1; x) * n!*(n-1)!/2.

a(n) = 2^(2*n + 1 + valuation(n, 2)) = 2^A292608(n). - Peter Luschny, Sep 23 2017

Example

1/8, 9/64, 75/128, 11025/2048, 178605/2048, 36018675/16384, 2608781175/32768, ...

Maple

seq(2^A292608(n), n=1..23); # Peter Luschny, Sep 23 2017

Mathematica

a[n_] := Gamma[n+1/2]^2/(2*n*Pi) // Denominator; Array[a, 30]
Table[(2*n)!^2 / (n * 2^(4*n+1) * n!^2), {n, 1, 20}] // Denominator (* Vaclav Kotesovec, Mar 11 2015 *)
b[n_] := 2*n + 1 + IntegerExponent[n, 2]; Table[2^b[n], {n, 1, 23}] (* Peter Luschny, Sep 23 2017 *)

Crossrefs

Cf. A255931 (numerators), A292608.

Sequence in context: A125110 A209990 A235425 * A043152 A044195 A153808

Adjacent sequences: A255929 A255930 A255931 * A255933 A255934 A255935

Keyword

frac,nonn

Author

Jean-François Alcover, Mar 11 2015

Status

approved