a(n) = Sum_{k=0..n} binomial(5*k,n-k) * Catalan(k).

Terms

a(0) =1a(1) =1a(2) =7a(3) =35a(4) =189a(5) =1092a(6) =6538a(7) =40278a(8) =253730a(9) =1626858a(10) =10582616a(11) =69669273a(12) =463319257a(13) =3107941405a(14) =21004392887a(15) =142882885210a(16) =977562617826