a(n) = n! if n is odd otherwise 0 (from the Taylor series for sin x).

Terms

a(0) =0a(1) =1a(2) =0a(3) =6a(4) =0a(5) =120a(6) =0a(7) =5040a(8) =0a(9) =362880a(10) =0a(11) =39916800a(12) =0a(13) =6227020800a(14) =0a(16) =0a(18) =0a(20) =0a(22) =0a(24) =0a(26) =0a(28) =0