OFFSET
1,3
COMMENTS
For even n, a(n)=0.
FORMULA
E.g.f. (for offset 2): sqrt(cosh(x))*exp(x^2/4).
Asymptotics (for even n): a(n)=exp(Pi^2/16)*(2^(n-2))*(n!)*(Pi^(-n))*n^(3/4)*(1+O(1/n)) [This formula is wrong. - Vaclav Kotesovec, Feb 15 2015]
If n is odd |a(n)| ~ exp(-Pi^2/16) * 2^(n+1/2) * n! / (sqrt(n) * Pi^(n+1)). - Vaclav Kotesovec, Feb 15 2015
MATHEMATICA
Rest[Rest[CoefficientList[Series[Sqrt[Cosh[x]]*E^(x^2/4), {x, 0, 20}], x] * Range[0, 20]!]] (* Vaclav Kotesovec, Feb 15 2015 *)
CROSSREFS
KEYWORD
easy,nice,sign
AUTHOR
Pietro Majer, Oct 27 2009
EXTENSIONS
More terms from Vaclav Kotesovec, Feb 15 2015
STATUS
approved