Closed forms for OEIS sequences?

[Eric W. Weisstein]

Can anyone get closed forms for the following?

Sum_{n=1..inf.} -(-1)^n*(e - (1 + n^(-1))^n).
http://www.research.att.com/~njas/sequences/?q=id:A114884

Integrate[Erf[x]^3/(E^(2*x^2)*x),{x,0,Infinity}].
http://www.research.att.com/~njas/sequences/?q=id:A115290

Coefficients of odd powers of 1/q in the solution series for Tan[x]/x=1
http://www.research.att.com/~njas/sequences/?q=id:A079330
http://www.research.att.com/~njas/sequences/?q=id:A088989

Coefficients of x^(2n-1) in series of 3Sin[x]/(2+Cos[x]).
http://www.research.att.com/~njas/sequences/?q=id:115184
http://www.research.att.com/~njas/sequences/?q=id:115185

?

Cheers,
-Eric