A165193

eigensequence of triangle A038208 where A038208 =
1
2, 2
4, 8, 4
8, 24, 24, 8
...
= triangle T, then Triangle T * any sequence S(n) as a vector say [1, 3, 5, 7,...] =
(1, 8, 48, 256, 1280,...); = A002697, where (Cf. comments); for example we have the
array
1, 3, 5, 3
3, 1, 3, 5
5, 3, 1, 3
3, 5, 3, 1
...total of terms = 48, where T * [1, 3, 5, 7,...] = (1, 8, 48, 256,...), thus the "48".