Column k=2 of Brent's table A381083 related to prime gaps 2n.

Terms

a(0) =0a(1) =0a(2) =2a(3) =4a(4) =6a(5) =56a(6) =40a(7) =40a(8) =92a(9) =624a(10) =504a(11) =10880a(12) =6688a(13) =7400a(14) =19312a(15) =113792a(16) =122400a(17) =3979008a(18) =2239104a(19) =2915840a(20) =5777920a(21) =56689920a(22) =55372800a(23) =110218240a(24) =78453760a(25) =65815552a(26) =125480960a(27) =2057036800a(28) =1776107520a(29) =137449159680