A340725 -id:A340725 - cp's OEIS frontend

A256191 Decimal expansion of Gamma(1/10).

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

Offset: 1

Iaroslav V. Blagouchine, Mar 19 2015

			9.513507698668731836292487177265402192550578626088377...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index to sequences related to the Gamma function

Cf. A175380, A246745, A340721, A340722.

Cf. A340723, A340724, A340725.

SetDefaultRealField(RealField(100)); Gamma(1/10); // G. C. Greubel, Mar 10 2018

Maple
```
evalf(GAMMA(1/10),100);
```
Mathematica
```
RealDigits[Gamma[1/10],10,100][[1]]
```
PARI
```
gamma(1/10)
```

From Vaclav Kotesovec, Apr 10 2024: (Start)
Equals 5^(1/4) * sqrt(1 + sqrt(5)) * Gamma(1/5) * Gamma(2/5) / (2^(7/10) * sqrt(Pi)).
Equals 2^(4/5) * sqrt(Pi) * Gamma(1/5) / Gamma(3/5). (End)

A216706 a(n) = Product_{k=1..n} (100 - 10/k).

Original entry on oeis.org

1, 90, 8550, 826500, 80583750, 7897207500, 776558737500, 76546504125000, 7558967282343750, 747497875698437500, 74002289694145312500, 7332954160601671875000, 727184620926332460937500, 72159089307305298046875000, 7164366724082454591796875000

Offset: 0

Michel Lagneau, Sep 16 2012

nonn

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A340725.

seq(product(100-10/k, k=1.. n), n=0..20);
seq((10^n/n!)*product(10*k+9, k=0.. n-1), n=0..20);

From Amiram Eldar, Aug 17 2025: (Start)
a(n) = 100^n * Gamma(n+9/10) / (Gamma(9/10) * Gamma(n+1)).
a(n) ~ c * 100^n / n^(1/10), where c = 1/Gamma(9/10) = 1/A340725 = 0.935778... . (End)

A025755 10th-order Patalan numbers (generalization of Catalan numbers).

Original entry on oeis.org

1, 1, 45, 2850, 206625, 16116750, 1316201250, 110936962500, 9568313015625, 839885253593750, 74749787569843750, 6727480881285937500, 611079513383472656250, 55937278532794804687500, 5154220664807521289062500, 477624448272163639453125000, 44478776745345238924072265625

Offset: 0

Olivier Gérard

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seq., Vol. 3 (2000), Article 00.2.4.
Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
Thomas M. Richardson, The Super Patalan Numbers, J. Int. Seq. 18 (2015), Article 15.3.3; arXiv preprint, arXiv:1410.5880 [math.CO], 2014.

Cf. A035278, A340725.

CoefficientList[Series[(11 -(1 - 100*x)^(1/10))/10, {x, 0, 20}], x] (* Vincenzo Librandi, Dec 29 2012 *)
a[n_] := 100^(n-1) * Pochhammer[9/10, n-1] / n!; a[0] = 1; Array[a, 26, 0] (* Amiram Eldar, Aug 20 2025 *)

G.f.: (11-(1-100*x)^(1/10))/10.
a(n) = 10^(n-1)*9*A035278(n-1)/n!, n >= 2, where 9*A035278(n-1) = (10*n-11)(!^10) = Product_{j=2..n} (10*j - 11). - Wolfdieter Lang
Conjecture: n*a(n) + 10*(-10*n+11)*a(n-1) = 0. - R. J. Mathar, Jul 28 2014
a(n) = 100^(n-1)*Pochhammer(9/10, n-1)/n! for n >= 1.  Maple confirms this satisfies Mathar's conjecture for n >= 2 (it's not true for n=1). - Robert Israel, Oct 05 2014
a(n) ~ 100^(n-1) / (Gamma(9/10) * n^(11/10)). - Amiram Eldar, Aug 20 2025

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A256191 Decimal expansion of Gamma(1/10).

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A216706 a(n) = Product_{k=1..n} (100 - 10/k).

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Maple

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A025755 10th-order Patalan numbers (generalization of Catalan numbers).

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Author

Keywords

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Programs

Mathematica

Formula