A090969 a(n) = 1/Integral_{x=0..1} (x^5 - x^6)^n.

1, 42, 858, 15504, 265650, 4417686, 72068304, 1160068104, 18490100706, 292486494300, 4599035681526, 71963547329856, 1121519754006288, 17419158268943970, 269767427275060200, 4167406330765934256

Offset: 0

Author

Al Hakanson (hawkuu(AT)excite.com), Feb 29 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..845

Crossrefs

Cf. A002457, A004355, A016921, A090816, A090957.

Programs

Magma

[Factorial(6*n+1)/(Factorial(n)*Factorial(5*n)): n in [0..20]]; // G. C. Greubel, Feb 03 2019

Maple

seq(factorial(6*n+1)/(factorial(n)*factorial(5*n)), n = 0 .. 16); # Emeric Deutsch, Jun 29 2009

Mathematica

Table[1/Beta[5*n+1, n+1], {n,0,20}] (* G. C. Greubel, Feb 03 2019 *)

PARI

vector(20, n, n--; (6*n+1)!/(n!*(5*n)!)) \\ G. C. Greubel, Feb 03 2019

Sage

[1/beta(5*n+1,n+1) for n in range(20)] # G. C. Greubel, Feb 03 2019

Formula

a(n) = A016921(n)*A004355(n). - R. J. Mathar, Jun 21 2009

a(n) = 1/B(5*n+1,n+1) = (6*n+1)!/(n! * (5*n)!), where B(p,q) is Euler's beta function (basically identical with R. J. Mathar's comment). - Emeric Deutsch, Jun 29 2009

a(n) ~ 2^(6*n+1) * 3^(6*n+3/2) * sqrt(n) / (sqrt(Pi) * 5^(5*n+1/2)). - Vaclav Kotesovec, Aug 15 2017

Extensions

Extended by Emeric Deutsch, Jun 29 2009