A380124
Total number of ways of partitioning n and any natural number less than n into the same number of parts.
Original entry on oeis.org
0, 0, 1, 3, 8, 17, 40, 78, 162, 308, 591, 1068, 1975, 3445, 6067, 10366, 17683, 29375, 48886, 79487, 129220, 206457, 328782, 516286, 808903, 1251135, 1929061, 2944622, 4478131, 6749574, 10139972, 15110286, 22440924, 33099258, 48645223, 71056244, 103449482, 149757609
Offset: 0
For example, a(4)=8:
4 and 1: (4,1),
4 and 2: (4,2) (3+1,1+1) (2+2,1+1),
4 and 3: (4,3) (3+1,2+1) (2+2,2+1) (2+1+1,1+1+1).
A380126
Total number of ways of partitioning n and any natural number less than or equal to n into the same number of parts, not treating partitions of n and itself in a different order as distinct.
Original entry on oeis.org
1, 1, 3, 6, 14, 26, 58, 106, 214, 394, 742, 1314, 2406, 4139, 7234, 12250, 20778, 34279, 56805, 91866, 148816, 236772, 375899, 588208, 919235, 1417538, 2180608, 3320197, 5038918, 7577850, 11363516, 16899942, 25056925, 36892553, 54136934, 78951553, 114783293, 165922204
Offset: 0
For example, a(4)=14:
4 and 1: (4,1),
4 and 2: (4,2) (3+1,1+1) (2+2,1+1),
4 and 3: (4,3) (3+1,2+1) (2+2,2+1) (2+1+1,1+1+1),
4 and 4: (4,4) (3+1,3+1) (3+1,2+2) (2+2,2+2) (2+1+1,2+1+1) (1+1+1+1,1+1+1+1).
Note that (3+1,2+2) and (2+2,3+1) are not both counted.
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