Geodesic
A restricted growth word approach to partitions with odd/even size blocks
Journal of integer sequences, Tome 20 (2017) no. 5
We use restricted growth words and multivariate generating functionology to obtain the ordinary generating function for the number of partitions of an $n$-set into $k$ blocks of odd (respectively, even) cardinality.
Classification : 05A18, 05A15
Keywords: set partition, restricted growth word, multivariate generating function 
@article{JIS_2017__20_5_a2,
     author = {Ehrenborg,  Richard and Hedmark,  Dustin and Hettle,  Cyrus},
     title = {A restricted growth word approach to partitions with odd/even size blocks},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {5},
     zbl = {1361.05013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a2/}
}
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Ehrenborg,  Richard; Hedmark,  Dustin; Hettle,  Cyrus. A restricted growth word approach to partitions with odd/even size blocks. Journal of integer sequences, Tome 20 (2017) no. 5. http://geodesic.mathdoc.fr/item/JIS_2017__20_5_a2/