Array read by antidiagonals: T(n,k) = n! * [x^n] exp(2*x + (k/2)*x^2), n >= 0, k >= 0.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =2a(5) =4a(6) =1a(7) =2a(8) =5a(9) =8a(10) =1a(11) =2a(12) =6a(13) =14a(14) =16a(15) =1a(16) =2a(17) =7a(18) =20a(19) =43a(20) =32a(21) =1a(22) =2a(23) =8a(24) =26a(25) =76a(26) =142a(27) =64a(28) =1a(29) =2