Triangle S(n, k) by rows: coefficients of 2^(n/2)*(x^(1/2)*d/dx)^n, where n =0, 2, 4, 6, ...

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =12a(5) =4a(6) =15a(7) =90a(8) =60a(9) =8a(10) =105a(11) =840a(12) =840a(13) =224a(14) =16a(15) =945a(16) =9450a(17) =12600a(18) =5040a(19) =720a(20) =32a(21) =10395a(22) =124740a(23) =207900a(24) =110880a(25) =23760a(26) =2112a(27) =64a(28) =135135a(29) =1891890