a(n) = Sum_{k=0..n} (3*k+2)*Catalan(k).

Terms

a(0) =2a(1) =7a(2) =23a(3) =78a(4) =274a(5) =988a(6) =3628a(7) =13495a(8) =50675a(9) =191673a(10) =729145a(11) =2786655a(12) =10691111a(13) =41150011a(14) =158825371a(15) =614483086a(16) =2382366586a(17) =9253540456a(18) =36001307656a(19) =140269835866a(20) =547245301906