A083012 a(n) = Sum_{k=0..n-1} 8^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.

0, 1, -7, 21, 49, -595, -1911, 39109, 165473, -4525731, -23883335, 805349237, 5097585297, -203564524787, -1503073984279, 69292329479205, 584713994953921, -30553447357629763, -290046835163027943, 16939595863125337813, 178676615255242261745

Offset: 0

Author

Benoit Cloitre, May 31 2003

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..432

Crossrefs

Cf. A001469.

Cf. A036968, A083007, A083008, A083009, A083010, A083011, A083013, A083014.

Programs

Mathematica

Range[0, 15]! CoefficientList[ Series[ 8x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x] + Exp[ 5x] + Exp[ 6x] + Exp[ 7x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)

PARI

a(n)=sum(k=0,n-1,8^k*binomial(n,k)*bernfrac(k))

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 28 2016