A178394 -id:A178394 - cp's OEIS frontend

A253182 The continued fraction expansion of e! (A178394).

4, 3, 1, 5, 38, 2, 1, 65, 1, 1, 2, 2, 3, 5, 1, 1, 38, 1, 1, 1, 5, 16, 1, 1, 1, 1, 5, 1, 97, 1, 1, 1, 1, 1, 1, 10, 4, 1, 6, 3, 3, 10, 6, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 4, 5, 1, 14, 2, 5, 12, 2, 2, 2, 2, 1, 3, 2, 1, 1, 2, 4, 1, 1, 6, 3, 1, 4, 2, 1, 1, 1, 1

Offset: 0

Robert G. Wilson v, Mar 23 2015

The increasing partial quotients (after the initial 4) are 3, 5, 38, 65, 97, 98, 239, 644, 3395, 11360, 14473, 263721, ..., .

			Gamma(e+1) = 4.2608204763570033817001212246457024649334243739593219749116...
= 4 + 1/(3 + 1/(1 + 1/(5 + 1/(38 + ...))))
= [a_0; a_1, a_2, a_3, ...] = [4; 3, 1, 5, 38, ...]

Cf. A178394, A255196.

Mathematica
```
ContinuedFraction[E!, 90]
```

default(realprecision, 100); contfrac(gamma(exp(1)+1)) \\ Michel Marcus, Mar 24 2015

A178840 Decimal expansion of the factorial of Golden Ratio.

Original entry on oeis.org

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

Offset: 1

Paolo P. Lava and Giorgio Balzarotti, Jun 17 2010

			1.44922960226989660037787979062976833708408989096667607533702385813891...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A111293, A178394, A178839.

Cf. A001622 (golden ratio).

SetDefaultRealField(RealField(100)); Gamma((Sqrt(5)-1)/2); // G. C. Greubel, Jan 21 2019

evalf(GAMMA(1+evalf((1+sqrt(5))/2,100)),106); # Golden ratio

RealDigits[Gamma[(Sqrt[5] - 1)/2], 10, 120][[1]] (* Vaclav Kotesovec, Jan 20 2019 *)

default(realprecision, 100); gamma((sqrt(5)-1)/2) \\ G. C. Greubel, Jan 21 2019

numerical_approx(gamma(1/golden_ratio), digits=100) # G. C. Greubel, Jan 21 2019

Factorial of Golden Ratio = Gamma(1 + phi) = Gamma((3 + sqrt(5))/2). - Bernard Schott, Jan 21 2019

Equals Gamma((sqrt(5) - 1)/2). - Vaclav Kotesovec, Jan 21 2019

A178839 Decimal expansion of the factorial of Euler-Mascheroni constant.

Original entry on oeis.org

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

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Jun 17 2010

			0.891152726131463856163339689050466491784711126227363757289227682281...

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A111293, A178394, A178840.

SetDefaultRealField(RealField(100)); R:=RealField(); Gamma(EulerGamma(R) + 1); // G. C. Greubel, Jan 21 2019

evalf(GAMMA(1+evalf(gamma,100)),106); # Euler-Mascheroni

RealDigits[Gamma[1 + EulerGamma], 10, 120][[1]] (* Vaclav Kotesovec, Jan 20 2019 *)

default(realprecision, 100); gamma(1 + Euler) \\ G. C. Greubel, Jan 21 2019

numerical_approx(gamma(1 + euler_gamma), digits=100) # G. C. Greubel, Jan 21 2019

Offset corrected by Vaclav Kotesovec, Jan 20 2019

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A253182 The continued fraction expansion of e! (A178394).

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A178840 Decimal expansion of the factorial of Golden Ratio.

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A178839 Decimal expansion of the factorial of Euler-Mascheroni constant.

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