Sequences | OEIS | EGF | reciprocal EGF | terms | reciprocal terms |
13-2 31-2 | A000108 A120588 A115140 A168491
| 2Φ+(-2+4x)Φ'-x Φ''=0
| | 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ... | 1, -1, 0, 1, 2, -2, -28, -65, 338, 3262, 4352, -113082, -879140, 1145012, 68641120, ... |
12-3 21-3 | A000110
| | | 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, ... | 1, -1, 0, 1, 1, -2, -9, -9, 50, 267, 413, -2180, -17731, -50533, 110176, ... |
132 213 312 | A111004
| | x ω'+ω''=0
| 1, 1, 2, 5, 16, 63, 296, 1623, 10176, 71793, 562848, 4853949, 45664896, 465403791, 5108121216, ... | 1, -1, 0, 1, 0, -3, 0, 15, 0, -105, 0, 945, 0, -10395, 0, ... |
123 | A049774
| | ω+ω'+ω''=0
| 1, 1, 2, 5, 17, 70, 349, 2017, 13358, 99377, 822041, 7477162, 74207209, 797771521, 9236662346, ... | 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, ... |