Well, surprise, surprise, there is already a sequence that gives the terms, though the signs don't always line up:

http://www.research.att.com/~njas/sequences/A009306

0, 1, 1, -1, -2, 9, 6, -155, 232, 3969, -20870, -118779, 1655028, 1610257, -143697722, ...

Okay, so now it's time to sit back and try to figure out why the sequences are related.

According to the description, the Sloane series is the "Expansion of ln(1+exp(x).x)", or in Mathematica: Log[ 1+Exp[ x ]*x ]

http://www.research.att.com/~njas/sequences/A009306

0, 1, 1, -1, -2, 9, 6, -155, 232, 3969, -20870, -118779, 1655028, 1610257, -143697722, ...

Okay, so now it's time to sit back and try to figure out why the sequences are related.

According to the description, the Sloane series is the "Expansion of ln(1+exp(x).x)", or in Mathematica: Log[ 1+Exp[ x ]*x ]

~ Jay Daniel Fox