[seqfan] An old sequence that seems to be wrong

[Neil Sloane]

Dear SeqFans, Many years ago Patrick Demichel
sent in a large number of Taylor series expansions that he obtained
by taking all combinations of log / exp / sin / arcsin / ...
of depth <= 3.
G. C. Greubel and Joerg Arndt recently noticed that A013568 does not match
its description.
which is
log(arcsin(x)/log(x+1))=x+7/5!*x^5-665/6!*x^6+219/7!*x^7-598/8!*x^8...,
so this is a mystery. Can anyone figure out what this is the Taylor
expansion of?
1, 0, 0, 0, 7, -665, 219, -598, 11570, -5357968, 995254, -4960662,
126624718, -783821598, 22344623929, -166137700653, 5222279193717,
-16426560893778654, 1561364880901471, -15643758252397591

One possibility would be to look at all the other depth-three
Taylor series that he submitted, and see which one is missing!
But perhaps an inspired guess would be quicker? I tried taking the exp
of his expression, but that did not seem to help.