A203142 -id:A203142 - cp's OEIS frontend

A203144 Decimal expansion of Gamma(5/8).

1, 4, 3, 4, 5, 1, 8, 8, 4, 8, 0, 9, 0, 5, 5, 6, 7, 7, 5, 6, 3, 6, 0, 1, 9, 7, 3, 9, 4, 5, 6, 4, 2, 3, 1, 3, 6, 6, 3, 2, 2, 0, 7, 7, 7, 2, 2, 0, 6, 6, 6, 7, 3, 3, 0, 7, 7, 0, 6, 7, 9, 8, 5, 8, 0, 9, 5, 0, 9, 4, 1, 9, 7, 3, 0, 2, 0, 9, 6, 9, 1, 4, 6, 3, 0, 9, 5, 6, 9, 6, 6, 5, 2, 5, 6, 3, 2, 2, 9

Offset: 1

N. J. A. Sloane, Dec 29 2011

			1.4345188480905567756360197394564231366322077722066673307706...

Index to sequences related to the Gamma function

RealDigits[Gamma[5/8],10,120][[1]] (* Harvey P. Dale, Sep 14 2018 *)

gamma(5/8) \\ Charles R Greathouse IV, Mar 25 2014

this * A203142 = 2^(3/4)*sqrt(Pi) * A068466. - R. J. Mathar, Jan 15 2021

A203125 Decimal expansion of (1/8)! = Gamma(9/8).

Original entry on oeis.org

9, 4, 1, 7, 4, 2, 6, 9, 9, 8, 4, 9, 7, 0, 1, 4, 8, 8, 0, 8, 7, 4, 0, 3, 7, 3, 0, 1, 5, 1, 8, 9, 1, 7, 0, 3, 0, 7, 6, 3, 0, 2, 4, 4, 8, 5, 1, 8, 6, 3, 4, 4, 9, 2, 6, 2, 2, 8, 9, 0, 9, 8, 7, 2, 2, 2, 0, 8, 2, 9, 5, 7, 1, 4, 9, 8, 6, 3, 3, 0, 1, 6, 0, 4, 1, 9, 1, 0, 7, 8, 3, 5, 1, 2, 9, 4, 6, 0, 6

Offset: 0

N. J. A. Sloane, Dec 29 2011

			.94174269984970148808740373015189170307630244851863449262289...

Index to sequences related to the Gamma function

Cf. A068467, A202623, A203126, A203142.

RealDigits[(1/8)!,10,120][[1]] (* Harvey P. Dale, May 30 2014 *)

gamma(9/8) \\ Charles R Greathouse IV, Mar 25 2014

Equals A203142/8. - R. J. Mathar, Jan 15 2021
A203144 *this *A231863 *A011006 = A068467. - R. J. Mathar, Jan 15 2021
Equals Integral_{x=0..oo} exp(-x^8) dx. - Ilya Gutkovskiy, Sep 18 2021

A034996 Related to octo-factorial numbers A045755.

Original entry on oeis.org

1, 36, 1632, 81600, 4308480, 235530240, 13189693440, 751812526080, 43438057062400, 2536782532444160, 149439552820346880, 8866746800673914880, 529276578255612149760, 31756594695336728985600, 1913864106972293533532160, 115788778471823758778695680, 7029059963701301121153761280

Offset: 1

Wolfdieter Lang

Convolution of A034977(n-1) with A025753(n), n >= 1.

Michael De Vlieger, Table of n, a(n) for n = 1..555
Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
Index entries for sequences related to factorial numbers.

Cf. A045755, A034977, A025753, A034904, A203142.

Rest@ CoefficientList[Series[(-1 + (1 - 64*x)^(-1/8))/8, {x, 0, 14}], x] (* Michael De Vlieger, Oct 13 2019 *)

a(n) = 8^(n-1)*A045755(n)/n!, where A045755(n) = (8*n-7)!^8 = Product_{j=1..n} (8*j-7).
G.f.: (-1+(1-64*x)^(-1/8))/8.
D-finite with recurrence: n*a(n) + 8*(-8*n+7)*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
a(n) ~ 8^(2*n-1) * n^(-7/8) / Gamma(1/8). - Amiram Eldar, Aug 18 2025

A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

Original entry on oeis.org

0, 2, 3, 0, 0, 4, 5, 8, 7, 8, 6, 2, 7, 3, 6, 0, 1, 0, 3, 1, 7, 9, 9, 2, 6, 0, 2, 1, 4, 5, 1, 4, 6, 9, 6, 2, 3, 1, 8, 6, 6, 7, 6, 4, 1, 4, 7, 5, 0, 8, 8, 3, 2, 9, 0, 9, 6, 3, 8, 0, 0, 6, 2, 0, 6, 5, 8, 1, 4, 5, 4, 7, 6, 3, 5, 4, 5, 5, 9, 4, 1, 4, 0, 3, 1, 5, 6, 6, 2, 3, 6, 1, 5, 5, 8, 9, 1, 9, 6, 7

Offset: 0

Jean-François Alcover, Aug 11 2014

			0.02300458786273601031799260214514696231866764147508832909638...

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 8.

Cf. A203142, A203143, A203144, A203146.

s = (Pi/(2*Sqrt[2]))*(Log[Gamma[1/8]*Gamma[3/8]/(Gamma[5/8]*Gamma[7/8])] - (EulerGamma + Log[2*Pi])); Join[{0}, RealDigits[s, 10, 99] // First]

(Pi/(2*sqrt(3)))*(log(Gamma(1/8)/Gamma(3/8)/(Gamma(5/8)/Gamma(7/8))) - (gamma + log(2*Pi))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.

A359533 Decimal expansion of Sum_{k>=0} (-1/64)^kbinomial(2k, k)^3(4k + 1)*H_k, where H_k is the k-th harmonic number (negated).

Original entry on oeis.org

2, 7, 6, 4, 2, 7, 2, 0, 4, 2, 4, 5, 9, 8, 6, 5, 7, 3, 0, 9, 2, 6, 3, 9, 8, 2, 5, 6, 1, 6, 8, 8, 9, 9, 4, 6, 7, 8, 3, 7, 4, 0, 7, 9, 5, 1, 9, 0, 4, 8, 5, 0, 6, 3, 0, 3, 2, 7, 7, 6, 9, 2, 0, 2, 7, 0, 3, 3, 7, 9, 6, 9, 4, 4, 5, 8, 9, 8, 7, 9, 7, 1, 0, 9, 8, 0, 1

Offset: 0

Stefano Spezia, Jan 04 2023

			0.276427204245986573092639825616889946783740795...

John M. Campbell, Applications of a class of transformations of complex sequences, arXiv:2212.13305 [math.NT], 2022. See p. 6.

Cf. A000796, A001008, A002805, A002897, A016639, A016813, A063448, A068465, A068466, A091925, A203142, A203143.

Cf. A359532.

First[RealDigits[N[(Gamma[1/8]Gamma[3/8]/(Gamma[1/4]Gamma[3/4]))^2/(6Sqrt[2]Pi)-4Log[2]/Pi,100]]]

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8)/(Gamma(1/4)*Gamma(3/4)))^2/(6*sqrt(2)*Pi).

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8))^2/(12*sqrt(2)*Pi^3).

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A203144 Decimal expansion of Gamma(5/8).

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A203125 Decimal expansion of (1/8)! = Gamma(9/8).

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A034996 Related to octo-factorial numbers A045755.

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A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

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A359533 Decimal expansion of Sum_{k>=0} (-1/64)^k*binomial(2*k, k)^3*(4*k + 1)*H_k, where H_k is the k-th harmonic number (negated).

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A359533 Decimal expansion of Sum_{k>=0} (-1/64)^kbinomial(2k, k)^3(4k + 1)*H_k, where H_k is the k-th harmonic number (negated).