A083010 a(n) = 6^n(B_n(1/6)-B_n(0)) where B_n(x) is the n-th Bernoulli polynomial.

0, 1, -5, 10, 25, -170, -575, 6370, 28225, -415826, -2294975, 41649850, 275622625, -5922729722, -45718037855, 1134081384850, 10004182986625, -281284596509858, -2791456543622015, 87722769712529770, 967282878165054625, -33597252908389628234, -407509096583935700255

Offset: 0

Author

Benoit Cloitre, May 31 2003

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..452

Crossrefs

Cf. A001469.

Cf. A036968, A083007, A083008, A083009, A083011, A083012, A083013, A083014.

Programs

Mathematica

Range[0, 15]! CoefficientList[ Series[ 6x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x] + Exp[ 5x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)

PARI

a(n)=sum(k=0,n-1,6^k*binomial(n,k)*bernfrac(k))

PARI

{a(n)=if(n<1, 0, n!*polcoeff( 6*x*(exp(x+x*O(x^n))-1)/(exp(6*x +x*O(x^n))-1), n))} /* Michael Somos, Aug 02 2006 */

Formula

E.g.f.: 6x(exp(x)-1)/(exp(6x)-1). - Michael Somos, Aug 02 2006

a(n) = Sum_{k=0..n-1} 6^k*B(k)*C(n,k) where B(k) is the k-th Bernoulli number and C(n,k) = binomial(n,k).