| m= | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
|---|
| P(0) | 1 | |
|---|
|
| P(1) | 1 | |
|---|
| P(2) | 1 | 1 | |
|---|
| P(3) | 1 | 1 | 1 | |
|---|
| P(4) | 1 | 2 | 1 | 1 | |
|---|
| P(5) | 1 | 2 | 2 | 1 | 1 | |
|---|
| P(6) | 1 | 3 | 3 | 2 | 1 | 1 | |
|---|
| P(7) | 1 | 3 | 4 | 3 | 2 | 1 | 1 | |
|---|
| P(8) | 1 | 4 | 5 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(9) | 1 | 4 | 7 | 6 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(10) | 1 | 5 | 8 | 9 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(11) | 1 | 5 | 10 | 11 | 10 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(12) | 1 | 6 | 12 | 15 | 13 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(13) | 1 | 6 | 14 | 18 | 18 | 14 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(14) | 1 | 7 | 16 | 23 | 23 | 20 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(15) | 1 | 7 | 19 | 27 | 30 | 26 | 21 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(16) | 1 | 8 | 21 | 34 | 37 | 35 | 28 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(17) | 1 | 8 | 24 | 39 | 47 | 44 | 38 | 29 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(18) | 1 | 9 | 27 | 47 | 57 | 58 | 49 | 40 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(19) | 1 | 9 | 30 | 54 | 70 | 71 | 65 | 52 | 41 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(20) | 1 | 10 | 33 | 64 | 84 | 90 | 82 | 70 | 54 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(21) | 1 | 10 | 37 | 72 | 101 | 110 | 105 | 89 | 73 | 55 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(22) | 1 | 11 | 40 | 84 | 119 | 136 | 131 | 116 | 94 | 75 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(23) | 1 | 11 | 44 | 94 | 141 | 163 | 164 | 146 | 123 | 97 | 76 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(24) | 1 | 12 | 48 | 108 | 164 | 199 | 201 | 186 | 157 | 128 | 99 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(25) | 1 | 12 | 52 | 120 | 192 | 235 | 248 | 230 | 201 | 164 | 131 | 100 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(26) | 1 | 13 | 56 | 136 | 221 | 282 | 300 | 288 | 252 | 212 | 169 | 133 | 101 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(27) | 1 | 13 | 61 | 150 | 255 | 331 | 364 | 352 | 318 | 267 | 219 | 172 | 134 | 101 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(28) | 1 | 14 | 65 | 169 | 291 | 391 | 436 | 434 | 393 | 340 | 278 | 224 | 174 | 135 | 101 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(29) | 1 | 14 | 70 | 185 | 333 | 454 | 522 | 525 | 488 | 423 | 355 | 285 | 227 | 175 | 135 | 101 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 | |
|---|
| P(30) | 1 | 15 | 75 | 206 | 377 | 532 | 618 | 638 | 598 | 530 | 445 | 366 | 290 | 229 | 176 | 135 | 101 | 77 | 56 | 42 | 30 | 22 | 15 | 11 | 7 | 5 | 3 | 2 | 1 | 1 |
|---|
P'(0) = 1
P'(1) = 1
P'(2) = 2
P'(3) = 3
P'(4) = 5
P'(5) = 7
P'(6) = 11
P'(7) = 15
P'(8) = 22
P'(9) = 30
P'(10) = 42
P'(11) = 56
P'(12) = 77
P'(13) = 101
P'(14) = 135
P'(15) = 176
P'(16) = 231
P'(17) = 297
P'(18) = 385
P'(19) = 490
P'(20) = 627
P'(21) = 792
P'(22) = 1002
P'(23) = 1255
P'(24) = 1575
P'(25) = 1958
P'(26) = 2436
P'(27) = 3010
P'(28) = 3718
P'(29) = 4565
P'(30) = 5604