[seqfan] binomial transform in A001519

[Richard J. Mathar]

A comment in A001519 by Witula says
"Moreover, a(n) is the second binomial transform of (0,1,0,5,0,25,...) ..."

However, if I start from [0,1,0,5,0,25...] and take the binomial transform
I get [0,1,2,8,24,80,...]
and after taking again the binomial transform I get
[0,1,4,17,72,305,..]
Can someone explain why the comment says that these operations result in
A001519, which is [1,1,2,5,13,34..]?

R. Mathar