A019704 -id:A019704 - cp's OEIS frontend

A007680 a(n) = (2n+1)*n!.

1, 3, 10, 42, 216, 1320, 9360, 75600, 685440, 6894720, 76204800, 918086400, 11975040000, 168129561600, 2528170444800, 40537905408000, 690452066304000, 12449059983360000, 236887827111936000, 4744158915944448000, 99748982335242240000

Offset: 0

N. J. A. Sloane

Denominators in series for sqrt(Pi/4)*erf(x): sqrt(Pi/4)*erf(x)= x/1 - x^3/3 + x^5/10 - x^7/42 + x^9/216 -+ ...
Appears to be the BinomialMean transform of A000354 (after truncating the first term of A000354). (See A075271 for the definition of BinomialMean.) - John W. Layman, Apr 16 2003
Number of permutations p of {1,2,...,n+2} such that max|p(i)-i|=n+1. Example: a(1)=3 since only the permutations 312,231 and 321 of {1,2,3} satisfy the given condition. - Emeric Deutsch, Jun 04 2003
Stirling transform of A000670(n+1) = [3, 13, 75, 541, ...] is a(n) = [3, 10, 42, 216, ...]. - Michael Somos, Mar 04 2004
Stirling transform of a(n) = [2, 10, 42, 216, ...] is A052875(n+1) = [2, 12, 74, ...]. - Michael Somos, Mar 04 2004
A related sequence also arises in evaluating indefinite integrals of sec(x)^(2k+1), k=0, 1, 2, ... Letting u = sec(x) and d = sqrt(u^2-1), one obtains a(0) = log(u+d) 2*k*a(k) = (2*k-1)*u^(2*k-1)*d + a(k-1). Viewing these as polynomials in u gives 2^k*k!*a(k) = a(0) + d*Sum(i=0..k-1){ (2*i+1)*i!*2^i*u^(2*i+1) }, which is easily proved by induction. Apart from the power of 2, which could be incorporated into the definition of u (or by looking at erf(ix/2)/ i (i=sqrt(-1)), the sum's coefficients form our series and are the reciprocals of the power series terms for -sqrt(-Pi/4)*erf(ix/2)). This yields a direct but somewhat mysterious relationship between the power series of erf(x) and integrals involving sec(x). - William A. Huber (whuber(AT)quantdec.com), Mar 14 2002
When written in factoradic ("factorial base"), this sequence from a(1) onwards gives the smallest number containing two adjacent digits, increasing when read from left to right, whose difference is n-1. - Christian Perfect, May 03 2016
a(n-1)^2 is the number of permutations p of [1..2n] such that Sum_{i=1..2n} abs(p(i)-i) = 2n^2-2. - Fang Lixing, Dec 07 2018
A standard series for the calculation of coordinates on a clothoid (also called cornuspiral):
  x = s*(a(0) - (tau^2/a(2)) + (tau^4/a(4)) - (tau^6/a(6)) + ...)
  y = s*((tau/a(1)) + (tau^3/a(3)) - (tau^5/a(5)) + ...).
  s is the arclength from the clothoids origin to the desired point p(x,y). The tangent at the clothoids origin intersects with the tangent at the point p(x,y) with an angle of tau. - Thomas Scheuerle, Oct 13 2021
a(n) = P_n(1) where P_n(x) is the Pidduck polynomials. - Michael Somos, May 27 2023

			G.f. = 1 + 3*x + 10*x^2 + 42*x^3 + 216*x^4 + 1320*x^5 + 9360*x^6 + ... - _Michael Somos_, Jan 01 2019

H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. Wirth, Systematisches Programmieren, 1975, exercise 9.3

Vincenzo Librandi, Table of n, a(n) for n = 0..400
Emeric Deutsch, Problem Q915, Math. Magazine, vol. 74, No. 5, 2001, p. 404.
H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy)
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
M. Z. Spivey and L. L. Steil, The k-Binomial Transforms and the Hankel Transform, J. Integ. Seqs. Vol. 9 (2006), #06.1.1.
Eric Weisstein's World of Mathematics, Erf
Wikipedia, Factorial base
Wikipedia, Pidduck polynomials
Jun Yan, Results on pattern avoidance in parking functions, arXiv:2404.07958 [math.CO], 2024. See p. 5.

From Johannes W. Meijer, Nov 12 2009: (Start)
Appears in A167546.
Equals the rows sums of A167556.
(End)
Cf. A019704, A099288.

a:=List([0..20],n->(2*n+1)*Factorial(n));; Print(a); # Muniru A Asiru, Jan 01 2019

[(2*n+1)*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Aug 20 2011

[(2*n+1)*factorial(n)$n=0..20]; # Muniru A Asiru, Jan 01 2019

Table[(2n + 1)*n!, {n, 0, 20}] (* Stefan Steinerberger, Apr 08 2006 *)

{a(n) = if( n<0, 0, (2*n+1) * n!)}; /* Michael Somos, Mar 04 2004 */

E.g.f.: (1+x)/(1-x)^2.
This is the binomial mean transform of A000354 (after truncating the first term). See Spivey and Steil (2006). - Michael Z. Spivey (mspivey(AT)ups.edu), Feb 26 2006
E.g.f.: (of aerated sequence) 1+x^2/2+sqrt(pi)*(x+x^3/4)*exp(x^2/4)*ERF(x/2). - Paul Barry, Apr 11 2010
G.f.: 1 + x*G(0), where G(k)= 1 + x*(k+1)/(1 - (k+2)/(k+2 + (k+1)/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 08 2013
a(n-2) = (A208528(n)+A208529(n))/2, for n>=2. - Luis Manuel Rivera Martínez, Mar 05 2014
D-finite with recurrence: (-2*n+1)*a(n) +n*(2*n+1)*a(n-1)=0. - R. J. Mathar, Jan 27 2020
Sum_{n>=0} 1/a(n) = sqrt(Pi)*erfi(1)/2 = A019704 * A099288 = A347910. - Amiram Eldar, Oct 07 2020
Sum_{n>=0} (-1)^n/a(n) = A347909 . - R. J. Mathar, Sep 30 2021

A087017 Decimal expansion of G(5/2) where G is the Barnes G-function.

Original entry on oeis.org

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

Offset: 0

Eric W. Weisstein, Jul 30 2003

			0.94757...

Eric Weisstein's World of Mathematics, Barnes G-Function
Wikipedia, Barnes G-function

Cf. A087013, A087014, A087015, A087016.

(E^(1/8)*Pi^(3/4))/(2^(23/24)*Glaisher^(3/2))
(* Or, since version 7.0, *) RealDigits[BarnesG[5/2], 10, 102] // First (* Jean-François Alcover, Jul 11 2014 *)

Pi^(3/4)*exp(3/2*zeta'(-1))/2^(23/24) \\ Charles R Greathouse IV, Dec 12 2013

Equals A087016 * A019704. - R. J. Mathar, Jul 24 2025

A190732 Decimal expansion of 2/sqrt(Pi).

Original entry on oeis.org

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

Offset: 1

Alonso del Arte, May 17 2011

According to Weisstein, some mathematicians define erf(z) without reference to this constant.
Also equals the average absolute value of the difference of two independent normally distributed random numbers with mean 0 and variance 1. - Jean-François Alcover, Oct 31 2014
Limit_{n->oo} 2^(1-2*n^2)*n*binomial(2*n^2, n^2) is proper to compute this constant (and also Pi) in a base of power 2. - Ralf Steiner, Apr 23 2017
A gauge point marked "c" on slide rule calculating devices in the 20th century. The Pickworth reference notes its use "in calculating the contents of cylinders". - Peter Munn, Aug 14 2020

			1.12837916709551257...

Chi Keung Cheung et al., Getting Started with Mathematica, 2nd Ed. New York: J. Wiley (2005) p. 79.
C. N. Pickworth, The Slide Rule, 24th Ed., Pitman, London (1945), p 53, Gauge Points.

G. C. Greubel, Table of n, a(n) for n = 1..5000
Steven R. Finch, Mean width of a regular simplex, arxiv:1111.4976 [math.MG], 2016, mu_2.
International Slide Rule Museum, Slide Rule Terms, Glossary and Encyclopedia, entry for "C".
Eric Weisstein's World of Mathematics, Erf
Index entries for transcendental numbers

Cf. A002161, A019704, A285388, A285389.

RealDigits[2/Sqrt[Pi], 10, 100][[1]]
RealDigits[Limit[2^(1 - 2 m^2) m Binomial[2 m^2, m^2], m -> Infinity], 10, 100][[1]] (* Ralf Steiner, Apr 22 2017 *)

2/sqrt(Pi) \\ G. C. Greubel, Jan 09 2017

Equals Sum_{n>=0} (-1)^n*Gamma((n+1)/2)/Gamma(n/2+1). - Jean-François Alcover, Jun 12 2013
Equals 1/A019704. - Michel Marcus, Jan 09 2017
Equals Limit_{n->infinity} A285388(n)/A285389(n). - Ralf Steiner, Apr 22 2017

A087654 Decimal expansion of D(1) where D(x) is the Dawson function.

Original entry on oeis.org

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

Offset: 0

Benoit Cloitre, Sep 25 2003

			0.5380795069127684191363874204075567547919750017539...

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 42, page 407.

G. C. Greubel, Table of n, a(n) for n = 0..5000
Eric Weisstein's World of Mathematics, Dawson's Integral.

RealDigits[ N[ Sqrt[Pi]*Erfi[1]/(2*E), 105]][[1]] (* Jean-François Alcover, Nov 08 2012 *)
RealDigits[DawsonF[1], 10, 120][[1]] (* Amiram Eldar, Jun 25 2023 *)

intnum(t=0, 1, exp(t^2))/exp(1) \\ Michel Marcus, Feb 28 2023

D(1) = (1/e)*Integral_{t=0..1} exp(t^2) dt.
Equals Integral_{x=0..oo} e^(-x^2) sin(2x) dx = 1F1(1;3/2;-1). - R. J. Mathar, Jul 10 2024
Equals A099288 * sqrt(Pi)/(2e) = A099288 *A019704 * A068985. - R. J. Mathar, Jul 10 2024

A217481 Decimal expansion of sqrt(2*Pi)/4.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Oct 04 2012

Equals Integral_{x>=0} sin(x^2) dx.
The generalizations are Integral_{x>=0} exp(i*x^n) dx =
  0.6266570686577501... + i*0.6266570686577501... for n=2,
  0.7733429420779898... + i*0.4464897557846246... for n=3,
  0.8374066967690864... + i*0.3468652110238094... for n=4,
  0.8732303655178185... + i*0.2837297451053993... for n=5,
and
  Gamma(1/n)*i^(1/n)/n in general, where i is the imaginary unit. - R. J. Mathar, Nov 14 2012
Mean of cycle length (and of tail length) in Pollard rho method for factoring n is sqrt(2*Pi)/4*sqrt(n). - Jean-François Alcover, May 27 2013
If m = (1/2) * sqrt(Pi/2), then the coordinates of the two asymptotic points of the Cornu spiral (also called clothoide) and whose Cartesian parametrization is: x = a * Integral_{0..t} cos(u^2) du and y = a * Integral_{0..t} sin(u^2) du are (a*m, a*m) and (-a*m, -a*m) (see the curve at the MathCurve link). - Bernard Schott, Mar 02 2020
Equals the limit as x approaches infinity of the Fresnel integrals Integral_{0..x} sin(t^2) dt and Integral_{0..x} cos(t^2) dt. - Bernard Schott, Mar 05 2020

			equals 0.62665706865775012560394132120276131... = A019727 / 4 = sqrt(A019675).

Muniru A Asiru, Table of n, a(n) for n = 0..2000
Robert Ferréol, Cornu spiral, Mathcurve.
I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products, (1980), page 420 (formulas 3.757.1, 3.757.2).
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (6.4.7)
Wikipedia, Fresnel Integral
Index entries for transcendental numbers

Apart from possible scaling sqrt(A019692/2^n) for n=0..7 are A019727, A002161, A069998, A019704, this sequence, A019706, A143149, A019710.

Sqrt(2*Pi(RealField(100)))/4; // G. C. Greubel, Sep 30 2018

Maple
```
evalf(sqrt(2*Pi))/4 ;
```

First@ RealDigits[N[Sqrt[2 Pi]/4, 105]] (* Michael De Vlieger, Sep 24 2018 *)

fpprec : 100; ev(bfloat(sqrt(2*%pi)))/4; /* Martin Ettl, Oct 04 2012 */

sqrt(2*Pi)/4 \\ Altug Alkan, Sep 08 2018

((sqrt(2*pi))/4).n(digits=100) # Jani Melik, Oct 05 2012

From A.H.M. Smeets, Sep 22 2018: (Start)
Equals Integral_{x >= 0} sin(4x)/sqrt(x) dx [see Gradsteyn and Ryzhik].
Equals Integral_{x >= 0} cos(4x)/sqrt(x) dx [see Gradsteyn and Ryzhik]. (End)
From Bernard Schott, Mar 02 2020: (Start)
Equals Integral_{x >= 0} cos(x^2) dx or Integral_{x >= 0} sin(x^2) dx.
Equals sqrt(Pi/8) or (1/2)*sqrt(Pi/2). (End)

A113550 a(n) = product of n successive numbers up to n, if n is odd a(n) = n(n-1).. = n!, if n is even a(n) = n(n+1)(n+2)... 'n' terms.

Original entry on oeis.org

1, 6, 6, 840, 120, 332640, 5040, 259459200, 362880, 335221286400, 39916800, 647647525324800, 6227020800, 1748648318376960000, 1307674368000, 6288139352883548160000, 355687428096000, 29051203810321992499200000, 121645100408832000, 167683548393178540705382400000

Offset: 1

Amarnath Murthy, Nov 03 2005

			a(3) = 3*2*1 = 6.
a(4) = 4*5*6*7 = 840.

G. C. Greubel, Table of n, a(n) for n = 1..350

Cf. A113549.

Cf. A019704, A073742, A092042, A092616, A333419, A367563.

n = 1; anfunc[n_] := (If [EvenQ[n], {an = n, Do[an = an*(n + i), {i, n - 1}]}, an = n! ]; an); Table[anfunc[n], {n, 1, 20}] (* Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006 *)

a(2n-1) = (2n-1)!, a(2n) = (4n-1)!/(2n-1)!.
a(2n-1)*a(2n) = (4n-1)!.
Sum_{n>=1} 1/a(n) = sinh(1) + (sqrt(Pi)/2) * (exp(1/4) * erf(1/2) - exp(-1/4) * erfi(1/2)). - Amiram Eldar, Aug 15 2025

More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006

A245885 Decimal expansion of Gamma(7/2), where Gamma is Euler's gamma function.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Aug 05 2014

			3.3233509704478425511840640312646472177454052302294758654008896...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Gamma Function
Wikipedia, Particular values of the Gamma function

Cf. A019704, A019718, A245884.

RealDigits[Gamma[7/2], 10, 104] // First

PARI
```
gammah(3) \\ Michel Marcus, Feb 11 2016
```

Gamma(7/2) = (15/8)*sqrt(Pi) = (5/2)*A245884.
Equals Integral_{x=0..oo} exp(-x^(2/5)) dx. - Ilya Gutkovskiy, Apr 10 2024
Equals 30*A019718. - Hugo Pfoertner, Apr 10 2024

A143149 Decimal expansion of 5sqrt(2Pi)/4.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Jul 27 2008

Upper bound using Shannon entropy arising in randomly-projected hypercubes.

			3.13328534328875...

David L. Donoho and Jared Tanner, Counting the faces of randomly-projected hypercubes and orthants, with applications, Discrete & computational geometry, Vol. 43 (2010), pp. 522-541, see p. 533; arXiv preprint, arXiv:0807.3590 [math.MG], 2008, see p. 10.
Wikipedia, Fresnel Integral.
Index entries for transcendental numbers.

Apart from possible scaling sqrt(A019692/2^n) for n=0..7 are A019727, A002161, A069998, A019704, A217481, A019706, this sequence, A019710.

Cf. A143148 (lower bound).

RealDigits[5*Sqrt[2*Pi]/4, 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

5*sqrt(2*Pi)/4 \\ Michel Marcus, Mar 06 2020

Equals 10*Integral_{x>=0} x*sin(x^4) dx or 10*Integral_{x>=0} x*cos(x^4) dx (Fresnel integrals).

Edited and a(100) corrected by Georg Fischer, Jul 16 2021

A194940 The Square Peg in the Round Hole constant.

Original entry on oeis.org

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

Offset: 0

William H. Richardson and Robert G. Wilson v, Sep 05 2011

Given a unit circle and a square of equal area, what is the amount of the square peg shavings (or filings) which would allow the peg to be inserted into the circle? It turns out to be not quite two sevenths.

			0.28445855040980187815920101812693174533005283078946269804587750...

Daniel Zwillinger, Editor, CRC Standard Mathematical Tables and Formulae, 31st Edition, Chapman & Hall/CRC, Boca Raton, Section 4.6.6 Circles, page 334 & figure 4.18, 2003.

G. C. Greubel, Table of n, a(n) for n = 0..10000
1728 Software Systems, Circle Sector, Segment, Chord and Arc Calculator.
Eric Weisstein's World of Mathematics, Circular Segment.
Wikipedia, Square peg in a round hole.
Wikipedia, Squaring the circle.
Wikipedia, Diagram of the problem.

Cf. A000796, A019704, A127454.

RealDigits[ 4*ArcCos[ Sqrt[Pi]/2] - Sqrt[ Pi(4 - Pi)], 10, 111][[1]]
RealDigits[Pi + Sqrt[ 2Pi(2 - Sqrt[Pi (4 - Pi)])] - 4 ArcSin[ Sqrt[Pi/4]], 10, 111][[1]] (* Robert G. Wilson v, Sep 20 2011 *)

4*acos(sqrt(Pi)/2) - sqrt(Pi*(4-Pi)) \\ G. C. Greubel, Mar 28 2017

Area = 4*arccos(sqrt(Pi)/2) - sqrt(Pi*(4-Pi)).

Area = Pi + sqrt(2*Pi(2 - sqrt(Pi*(4 - Pi)))) - 4*arcsin(sqrt(Pi/4)). - Robert G. Wilson v, Mar 19 2014

A245884 Decimal expansion of Gamma(5/2), where Gamma is Euler's gamma function.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Aug 05 2014

			1.32934038817913702047362561250585888709816209209179034616...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Gamma Function.
Wikipedia, Particular values of the Gamma function.

Cf. A019704, A245885.

RealDigits[Gamma[5/2], 10, 100] // First

PARI
```
gammah(2) \\ Michel Marcus, Feb 11 2016
```

Equals (3/4)*sqrt(Pi) = (3/2)*A019704.
Equals Sum_{k>=1} (k+1/2)!/(k+2)!. - Amiram Eldar, Jun 19 2023
Equals Integral_{x=0..oo} exp(-x^(2/3)) dx. - Ilya Gutkovskiy, Apr 10 2024

cp's OEIS Frontend

A007680 a(n) = (2n+1)*n!.

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A087017 Decimal expansion of G(5/2) where G is the Barnes G-function.

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A190732 Decimal expansion of 2/sqrt(Pi).

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A087654 Decimal expansion of D(1) where D(x) is the Dawson function.

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A217481 Decimal expansion of sqrt(2*Pi)/4.

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A113550 a(n) = product of n successive numbers up to n, if n is odd a(n) = n*(n-1)*.. = n!, if n is even a(n) = n(n+1)(n+2)... 'n' terms.

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Formula

Extensions

A245885 Decimal expansion of Gamma(7/2), where Gamma is Euler's gamma function.

A113550 a(n) = product of n successive numbers up to n, if n is odd a(n) = n(n-1).. = n!, if n is even a(n) = n(n+1)(n+2)... 'n' terms.

A143149 Decimal expansion of 5sqrt(2Pi)/4.