A083013 a(n) = Sum_{k=0..n-1} 9^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.

0, 1, -8, 28, 64, -980, -3104, 81172, 339328, -11878244, -61958240, 2674671076, 16735235392, -855605816468, -6245150369696, 368601472639540, 3074742020313856, -205700802920736452, -1930357641628367072, 144338957346266943364, 1505019970814899568320

Offset: 0

Author

Benoit Cloitre, May 31 2003

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..424

Crossrefs

Cf. A001469.

Cf. A036968, A083007, A083008, A083009, A083010, A083011, A083012, A083014.

Programs

Mathematica

Range[0, 15]! CoefficientList[ Series[ 9x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x] + Exp[ 5x] + Exp[ 6x] + Exp[ 7x] + Exp[ 8x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)
Table[Sum[9^k BernoulliB[k]Binomial[n,k],{k,0,n-1}],{n,0,20}] (* Harvey P. Dale, Apr 13 2016 *)

PARI

a(n)=sum(k=0,n-1,9^k*binomial(n,k)*bernfrac(k))

Extensions

Offset changed to 0 by Seiichi Manyama, Sep 28 2016