Eulerian Sequences

There are 5! permutations of the numbers 1,2,3,4,5. How many of them are there in which exactly 2 of the numbers are greater than their predecessor?

12543
13542
13254
14253
14325
14352
14532
15243
15324
15342
15423

21354
21435
21453
21534
23154
23541
24153
24315
24351
24531
25143
25314
25341
25413

31254
31425
31452
31524
32145
32415
32451
32514
34152
34215
34251
34512
35142
35241
35214
35412

41253
41325
41352
41523
42135
42315
42351
42513
43125
43512
45132
45231
45213
45312

51243
51342
51324
51423
52134
52314
52341
52413
53124
53412
54123

So A(5,2)=66
The numbers A(n,k) are called Eulierian numbers. If we fix k and let n run through the integers greater than k, we get what is called an Eulerian Sequence.