Expansion of Sum_{k>=0} k! * ( x/(1+x^2) )^k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =20a(5) =103a(6) =630a(7) =4475a(8) =36232a(9) =329341a(10) =3320890a(11) =36787889a(12) =444125628a(13) =5803850515a(14) =81625106990