Binomial transform of expansion of exp(cosh(x)), A005046.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =11a(5) =31a(6) =107a(7) =379a(8) =1556a(9) =6556a(10) =31007a(11) =150349a(12) =801341a(13) =4373461a(14) =25853102a(15) =156297964a(16) =1012382291a(17) =6698486371a(18) =47089993967a(19) =337789490599