login
A198629
Alternating sums of powers of 1,2,...,6, divided by 3.
2
0, 1, 7, 45, 287, 1821, 11487, 72045, 449407, 2789181, 17230367, 105996045, 649630527, 3968504541, 24174772447, 146908944045, 890924667647, 5393590283901, 32604530573727, 196853323284045, 1187295678104767, 7154833690143261
OFFSET
0,3
COMMENTS
For the e.g.f.s and o.g.f.s of such alternating power sums see A196847 (even case) and A196848 (odd case).
LINKS
FORMULA
a(n)=sum(((-1)^j)*j^n,j=1..6)/3, n>=0.
E.g.f.: sum(((-1)^j)*exp(j*x),j=1..6)/3 = exp(x)*(exp(6*x)-1)/(3*(exp(x)+1)).
O.g.f.: sum(((-1)^j)/(1-j*x),j=1..6)/3 = x*(1-14*x+73*x^2-168*x^3+148*x^4)/
product(1-j*x,j=1..6). See A196847 for a formula for the coefficients of the numerator polynomial.
MAPLE
A198629 := proc(n)
(-3^n+4^n-1+2^n-5^n+6^n)/3 ;
end proc:
seq(A198629(n), n=0..20) ; # R. J. Mathar, May 11 2022
MATHEMATICA
Table[Total[Times@@@Partition[Riffle[Range[6]^n, {-1, 1}, {2, -1, 2}], 2]]/3, {n, 0, 30}] (* Harvey P. Dale, Jul 17 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 28 2011
STATUS
approved