a(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k), n>=1.

Terms

a(0) =1a(1) =3a(2) =25a(3) =111a(4) =456a(5) =2697a(6) =15961a(7) =86247a(8) =495781a(9) =3003738a(10) =17946798a(11) =107667969a(12) =660458787a(13) =4081397547a(14) =25274724105a(15) =157744019799a(16) =991384251102