[seqfan] Re: exp(sin(x))

[franktaw at netscape.net]

Never mind. I had no sooner walked away from the computer than I 
realized that this is completely straightforward.

Franklin T. Adams-Watters

-----Original Message-----
From: franktaw at netscape.net

A003724, the number of set partitions of n objects into odd blocks, is
the exponential expansion of exp(sinh(x)).

It appears that A002017, the expansion of exp(sin(x)), is the number of
set partitions of n objects with an even number of parts of size == 3
(mod 4), minus the number of such partitions with an odd number of
parts of size == 3 (mod 4). I have manually verified this through n =
8. Can someone confirm (i.e., prove) it?

Franklin T. Adams-Watters