%I #14 Sep 22 2017 07:46:17
%S 0,1,-31,2060,-242972,44808921,-11905513623,4306834677808,
%T -2035350070549744,1217544864812657225,-899267301542329562375,
%U 803729476432302540694956,-854933675015747706872042556,1067328531318200947345698975505,-1545426104859564195269842899644047
%N a(n) = 1/2*((-1)^n*E(2*n-1,n) - E(2*n-1,0)), where E(n,x) is the Euler polynomial.
%D M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
%F a(n) = 1^(2*n-1) - 2^(2*n-1) + ... + (-1)^n*(n-1)^(2*n-1).
%F |a(n)| ~ 1/(1+e^(-2))*(n-1)^(2*n-1) = 0.88079707...*(n-1)^(2*n-1) as n goes to infinity.
%t Table[((-1)^n EulerE[2n-1,n]-EulerE[2n-1,0])/2,{n,10}]
%t Map[Total[(Map[(-1)^# (#-1)&,Range[#]])^(2#-1)]&,Range[10]]
%t (* _Peter J. C. Moses_, Sep 21 2017 *)
%o (PARI) a(n) = sum(k=1, n-1, (-1)^(k+1)*k^(2*n-1)); \\ _Michel Marcus_, Sep 22 2017
%Y Cf. A143074, A157805.
%K sign
%O 1,3
%A _Vladimir Shevelev_, Sep 21 2017
%E More terms from _Peter J. C. Moses_, Sep 21 2017