A086400 (1/p)*(M(p)-1) where p runs through the odd primes and M(p)=A001006(p) is the p-th Motzkin number.

1, 4, 18, 527, 3218, 138634, 957857, 49120018, 20473889132, 156766505690, 74324776, 203270, 4686290685410776, 37541445026997947, 2445882966702428971, 13279375056930183, 42712, 743757817682170309535791