A124523 Binomial transform of A084239.
1, 3, 8, 20, 49, 119, 289, 707, 1749, 4379, 11092, 28412, 73573, 192535, 508918, 1357770, 3653343, 9905437, 27040975, 74269569, 205091177, 569078255, 1585839062, 4436191950, 12452408525, 35062157207, 99000292173, 280242836387, 795124827781, 2260758570327
Offset: 0