A090957 a(n) = 1/(Integral_{x=0..1} (x^4 - x^5)^n dx).

1, 30, 495, 7280, 101745, 1381380, 18407025, 242082720, 3153092085, 40763504210, 523886186670, 6700599687600, 85360889543475, 1083790852008480, 13721016740550360, 173280964190422080, 2183615911571190525

Offset: 0

Author

Al Hakanson (hawkuu(AT)excite.com), Feb 27 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..915

Crossrefs

Cf. A002457, A090816, A090969.

Programs

Magma

[Factorial(5*n+1)/(Factorial(n)*Factorial(4*n)): n in [0..20]]; // G. C. Greubel, Feb 03 2019

Maple

seq(factorial(5*n+1)/(factorial(n)*factorial(4*n)), n = 0 .. 16); # Emeric Deutsch, Jul 03 2009

Mathematica

Table[1/Integrate[(x^4-x^5)^n,{x,0,1}],{n,0,20}] (* Harvey P. Dale, Jan 02 2013 *)
Table[1/Beta[4*n+1,n+1], {n,0,20}] (* G. C. Greubel, Feb 03 2019 *)

PARI

for (n = 0, 20, pol = (x^4 - x^5)^n; s = 0; for (i = 4*n, 5*n, s += polcoeff(pol, i)/(i + 1)); print(1/s)); \\ David Wasserman, Feb 22 2006

PARI

vector(20, n, n--; (5*n+1)!/(n!*(4*n)!)) \\ G. C. Greubel, Feb 03 2019

Sage

[1/beta(4*n+1,n+1) for n in range(20)] # G. C. Greubel, Feb 03 2019

Formula

a(n) = 1/B(4*n+1,n+1) = (5*n+1)!/(n! * (4*n)!), where B(p,q) is Euler's beta function. - Emeric Deutsch, Jul 03 2009

a(n) ~ sqrt(n)*5^(5*n+3/2) / (sqrt(Pi)*2^(8*n+3/2)). - Vaclav Kotesovec, Aug 15 2017

Extensions

More terms from David Wasserman, Feb 22 2006