a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(k,2*(n-k)).

Terms

a(0) =1a(1) =6a(2) =24a(3) =104a(4) =480a(5) =2112a(6) =8752a(7) =34848a(8) =135168a(9) =513792a(10) =1920000a(11) =7071744a(12) =25728256a(13) =92622336a(14) =330405888a(15) =1169217536a(16) =4108296192a(17) =14344470528a(18) =49802211328a(19) =172027060224a(20) =591476293632