a(n) = Sum_{k=0..2*n} (k+1)*T(n,k), T given by A027960.

Terms

a(0) =1a(1) =10a(2) =40a(3) =124a(4) =340a(5) =868a(6) =2116a(7) =4996a(8) =11524a(9) =26116a(10) =58372a(11) =129028a(12) =282628a(13) =614404a(14) =1327108a(15) =2850820a(16) =6094852a(17) =12976132a(18) =27525124a(19) =58195972a(20) =122683396a(21) =257949700a(22) =541065220a(23) =1132462084a(24) =2365587460a(25) =4932501508a(26) =10267656196a(27) =21340618756a(28) =44291850244a(29) =91804925956