A292706 a(n) = 1/2*((-1)^n*E(2*n-1,n) - E(2*n-1,0)), where E(n,x) is the Euler polynomial.

0, 1, -31, 2060, -242972, 44808921, -11905513623, 4306834677808, -2035350070549744, 1217544864812657225, -899267301542329562375, 803729476432302540694956, -854933675015747706872042556, 1067328531318200947345698975505, -1545426104859564195269842899644047

Offset: 1

Author

Vladimir Shevelev, Sep 21 2017

Keywords

• sign

References

• M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.

Crossrefs

Cf. A143074, A157805.

Programs

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 *)

PARI

a(n) = sum(k=1, n-1, (-1)^(k+1)*k^(2*n-1)); \\ Michel Marcus, Sep 22 2017

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.

Extensions

More terms from Peter J. C. Moses, Sep 21 2017