OFFSET
1,3
COMMENTS
Conjecture. For n >= 2, a(n) is divisible by n(n-1)/2, moreover, for odd n, a(n) is divisible by n^2(n-1)/2.
REFERENCES
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
FORMULA
a(n) = (-1)^n*(1^(2*n) - 2^(2*n) + ... +(-1)^n*(n-1)^(2*n)).
a(n) ~ c * n^(2*n), where c = A349003/2 = 1/(1 + exp(2)) = 0.1192029220221175559402708586976... - Vaclav Kotesovec, Nov 05 2021
MATHEMATICA
Table[EulerE[2 n, n]/2, {n, 15}] (* Michael De Vlieger, Sep 23 2017 *)
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 23 2017
EXTENSIONS
More terms from Peter J. C. Moses, Sep 23 2017
STATUS
approved