A259437
a(n) = Sum_{k=0..n} p(k)^n, where p(k) is the partition function A000041.
Original entry on oeis.org
1, 2, 6, 37, 724, 20209, 1905630, 191250531, 57659285287, 20931112851787, 17697850924585423, 17720783665888137843, 44421728434157120665320, 117208746422032553556330253, 679595843556865572365153402674, 4907378683411420479410336076467628
Offset: 0
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Table[Sum[PartitionsP[k]^n,{k,0,n}],{n,0,15}]
A259438
a(n) = Sum_{k=0..n} p(k)^(n-k), where p(k) is the partition function A000041.
Original entry on oeis.org
1, 2, 3, 5, 10, 25, 78, 301, 1414, 7964, 53408, 426116, 4028890, 44697755, 576491980, 8617031811, 149425700853, 3004591733938, 69763130950599, 1860330686377532, 56746090401472922, 1975156902590115291, 78299783319570477185, 3529323014512112469681
Offset: 0
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Table[Sum[PartitionsP[k]^(n-k),{k,0,n}],{n,0,25}]
A265095
a(n) = Sum_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009).
Original entry on oeis.org
1, 2, 3, 11, 27, 270, 4366, 82491, 1762107, 135979835, 10135979835, 753144350523, 130499482241148, 20953464347912316, 6242774737775732860, 2960555481288609431503, 1211886375095917784137679, 719537152598665509899534287, 851154233276178632011679465423
Offset: 0
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Table[Sum[PartitionsQ[k]^k, {k,0,n}], {n,0,20}]
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