A097085 Row sums of triangle A097084, in which the n-th diagonal equals the n-th row transformed by triangle A008459 (squared binomial coefficients).

1, 2, 4, 10, 26, 70, 204, 618, 1908, 6010, 19316, 63034, 208210, 695594, 2346748, 7983450, 27364842, 94439262, 327922692, 1145029314, 4018618374, 14169874350, 50179643628, 178410716622, 636679332588, 2279906714610, 8190512723940