OFFSET
1,3
REFERENCES
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
FORMULA
a(n) = 1^(2*n-1) - 2^(2*n-1) + ... + (-1)^n*(n-1)^(2*n-1).
|a(n)| ~ 1/(1+e^(-2))*(n-1)^(2*n-1) = 0.88079707...*(n-1)^(2*n-1) as n goes to infinity.
MATHEMATICA
Table[((-1)^n EulerE[2n-1, n]-EulerE[2n-1, 0])/2, {n, 10}]
Map[Total[(Map[(-1)^# (#-1)&, Range[#]])^(2#-1)]&, Range[10]]
(* Peter J. C. Moses, Sep 21 2017 *)
PROG
(PARI) a(n) = sum(k=1, n-1, (-1)^(k+1)*k^(2*n-1)); \\ Michel Marcus, Sep 22 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Shevelev, Sep 21 2017
EXTENSIONS
More terms from Peter J. C. Moses, Sep 21 2017
STATUS
approved