# [seqfan] Requesting contact with Peter Bala (or someone else who can give a source)

William Keith william.keith at gmail.com
Fri Feb 3 10:42:07 CET 2012

I dropped a note on Peter's Wiki userpage a couple of days ago, as the
guidelines suggest, but haven't gotten a reply from there.

Mr. Bala added a comment to the formula section of A036969 concerning an
expansion for the central factorial numbers* as the connection coefficients
in x^n = \sum T(n,k) \prod (x-i^2). The expansion is quite correct (I can
derive it from the generating function in Stanley EC2 and standard facts on
combinatorics); I'm just wondering if it's sourced from somewhere in the
lit.  Riordan, who defined the central factorial numbers in 1968 in his
book _Combinatorial Identities_, gives a different expansion that gives
them as every even-indexed entry.

If Mr. Bala could get in touch with me off-list, or if someone who knows a
source for the particular definition described could point me to one, I
would be most appreciative.

Cordially,
William Keith

*P.S. There are quite a lot of very differently defined sequences with this
verbal title.