Triangle read by rows: row n (n>=0) has g.f. Sum_{i=1..n} n!*x^i*(1+x)^(n-i)/(n+1-i).

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =1a(5) =3a(6) =0a(7) =2a(8) =7a(9) =11a(10) =0a(11) =6a(12) =26a(13) =46a(14) =50a(15) =0a(16) =24a(17) =126a(18) =274a(19) =326a(20) =274a(21) =0a(22) =120a(23) =744a(24) =1956a(25) =2844a(26) =2556a(27) =1764a(28) =0a(29) =720