Convolution of Catalan numbers and powers of -1.

Terms

a(0) =1a(1) =0a(2) =2a(3) =3a(4) =11a(5) =31a(6) =101a(7) =328a(8) =1102a(9) =3760a(10) =13036a(11) =45750a(12) =162262a(13) =580638a(14) =2093802a(15) =7601043a(16) =27756627a(17) =101888163a(18) =375750537a(19) =1391512653a(20) =5172607767a(21) =19293659253a(22) =72188904387a(23) =270870709263