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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. 1
8, 64, 128, 2048, 2048, 16384, 32768, 1048576, 524288, 4194304, 8388608, 134217728, 134217728, 1073741824, 2147483648, 137438953472, 34359738368, 274877906944, 549755813888, 8796093022208, 8796093022208, 70368744177664, 140737488355328 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Mar 11 2015

STATUS

approved

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Last modified April 20 04:42 EDT 2019. Contains 322294 sequences. (Running on oeis4.)