a(n) = (5!)^3 * [z^5] hypergeom([], [1,1], z)^n.

Terms

a(0) =0a(1) =1a(2) =2252a(3) =111753a(4) =1297504a(5) =7120505a(6) =25461756a(7) =70250257a(8) =163191008a(9) =335493009a(10) =629597260a(11) =1100904761a(12) =1819504512a(13) =2871901513a(14) =4362744764a(15) =6416555265a(16) =9179454016a(17) =12820890017a(18) =17535368268a(19) =23544177769a(20) =31097119520a(21) =40474234521a(22) =51987531772a(23) =65982716273a(24) =82840917024a(25) =102980415025a(26) =126858371276a(27) =154972554777