a(n) = (1/(n+1)) * Sum_{k=0..n} (k+1)^4 * binomial(2*n-k,n-k).

Terms

a(0) =1a(1) =9a(2) =45a(3) =190a(4) =750a(5) =2871a(6) =10829a(7) =40560a(8) =151470a(9) =565250a(10) =2110482a(11) =7889598a(12) =29541200a(13) =110812275a(14) =416458125a(15) =1568143680a(16) =5915896470a(17) =22359073950a(18) =84655998150a(19) =321071107500