Triangle where T(n,k) = n!*[x^k] ( x/(2*x + log(1-x)) )^(n+1), for n>=k>=0, read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =6a(7) =12a(8) =23a(9) =41a(10) =24a(11) =60a(12) =130a(13) =255a(14) =469a(15) =120a(16) =360a(17) =870a(18) =1860a(19) =3679a(20) =6889a(21) =720a(22) =2520a(23) =6720a(24) =15540a(25) =32858a(26) =65247a(27) =123605a(28) =5040a(29) =20160