a(n) = (n+1)*(n+2)*(n+9)*3^n/18.

Terms

a(0) =1a(1) =10a(2) =66a(3) =360a(4) =1755a(5) =7938a(6) =34020a(7) =139968a(8) =557685a(9) =2165130a(10) =8227494a(11) =30705480a(12) =112842639a(13) =409209570a(14) =1466777160a(15) =5203870272a(16) =18294856425a(17) =63795240522a(18) =220829678730a(19) =759344158440