Triangle read by rows: number of permutations of 1..n by length of longest run.

Terms

a(0) =2a(1) =2a(2) =4a(3) =2a(4) =12a(5) =10a(6) =2a(7) =16a(8) =70a(9) =32a(10) =2a(11) =20a(12) =134a(13) =442a(14) =122a(15) =2a(16) =24a(17) =198a(18) =1164a(19) =3108a(20) =544a(21) =2a(22) =28a(23) =274a(24) =2048a(25) =10982a(26) =24216a(27) =2770a(28) =2a(29) =32