a(n) = n!*[x^n] cosh(x/(1-x))/(1-x).

Terms

a(0) =1a(1) =1a(2) =3a(3) =15a(4) =97a(5) =745a(6) =6571a(7) =65359a(8) =723969a(9) =8842257a(10) =118091251a(11) =1712261551a(12) =26786070433a(13) =449634481465