Alternating sum along antidiagonals of the array of A129952 and its iterated differences.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =10a(5) =23a(6) =60a(7) =139a(8) =326a(9) =735a(10) =1648a(11) =3635a(12) =7962a(13) =17287a(14) =37316a(15) =80091a(16) =171118a(17) =364079a(18) =771864a(19) =1631107a(20) =3436994a(21) =7223511a(22) =15146092a(23) =31690283a(24) =66176790a(25) =137945983a(26) =287076800a(27) =596523219a(28) =1237785706a(29) =2565049895