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A083013
a(n) = Sum_{k=0..n-1} 9^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number.
9
0, 1, -8, 28, 64, -980, -3104, 81172, 339328, -11878244, -61958240, 2674671076, 16735235392, -855605816468, -6245150369696, 368601472639540, 3074742020313856, -205700802920736452, -1930357641628367072, 144338957346266943364, 1505019970814899568320
OFFSET
0,3
LINKS
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 *)
PROG
(PARI) a(n)=sum(k=0, n-1, 9^k*binomial(n, k)*bernfrac(k))
KEYWORD
sign
AUTHOR
Benoit Cloitre, May 31 2003
EXTENSIONS
Offset changed to 0 by Seiichi Manyama, Sep 28 2016
STATUS
approved