Triangle read by rows: T(n,k) = binomial(n+1,k+1)*Stirling2(n+k,k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =3a(5) =7a(6) =0a(7) =6a(8) =60a(9) =90a(10) =0a(11) =10a(12) =310a(13) =1505a(14) =1701a(15) =0a(16) =15a(17) =1260a(18) =14490a(19) =46620a(20) =42525a(21) =0a(22) =21a(23) =4445a(24) =105875a(25) =716205a(26) =1727110a(27) =1323652a(28) =0a(29) =28