OFFSET
0,2
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).
FORMULA
a(n) = sum(((-1)^(j+1))*j^n,j=1..5) = 1-2^n+3^n-4^n+5^n.
E.g.f.: sum(((-1)^(j+1))*exp(j*x),j=1..5) =
exp(x)*(1+exp(5*x))/(1+exp(x)).
O.g.f.: sum(((-1)^(j+1))/(1-j*x),j=1..5) =
(1-12*x+55*x^2-114*x^3+94*x^4)/product(1-j*x,j=1..5).
A formula for the numbers of the numerator polynomial is given in A196848.
MAPLE
A198628 := proc(n)
3^n-4^n+1-2^n+5^n ;
end proc:
seq(A198628(n), n=0..20) ; # R. J. Mathar, May 11 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 27 2011
STATUS
approved