a(n) = Sum_{k=0..n} binomial(4*n+1,k).

Terms

a(0) =1a(1) =6a(2) =46a(3) =378a(4) =3214a(5) =27896a(6) =245506a(7) =2182396a(8) =19548046a(9) =176142312a(10) =1594831736a(11) =14497410186a(12) =132224930146