k

$E_1\left(k,0\right)$

$E_1\left(k,1\right)$

$E_1\left(k,2\right)$

$E_1\left(k,3\right)$

$E_1\left(k,4\right)$

$E_1\left(k,5\right)$

$E_1\left(k,6\right)$

$E_1\left(k,7\right)$

${\displaystyle \sum _{l=0}^k}{E}_1\left(k,l\right)$

0

1

1 = 0!

1

1

1 = 1!

2

1

1

2 = 2!

3

1

4

1

6 = 3!

4

1

11

11

1

24 = 4!

5

1

26

66

26

1

120 = 5!

6

1

57

302

302

57

1

720 = 6!

7

1

120

1191

2416

1191

120

1

5040 = 7!

8

1

247

4293

15 619

15 619

4293

247

1

40 320 = 8!

9

1

502

14 608

88 234

156 190

88 234

14 608

502

1

362 880 = 9!