A356283
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
Original entry on oeis.org
1, 4, 22, 131, 807, 5066, 32188, 206242, 1329733, 8614685, 56024538, 365491218, 2390613557, 15671221522, 102925324569, 677110860689, 4460956827127, 29427611146335, 194348311824025, 1284856925961827, 8502252246841668, 56309476194587377, 373220349572126265
Offset: 0
-
Table[Sum[PartitionsQ[k]*Binomial[3*n, n-k], {k, 0, n}], {n, 0, 30}]
A356289
a(n) = Sum_{k=0..n} binomial(2*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
Original entry on oeis.org
1, 4, 18, 82, 372, 1676, 7500, 33358, 147570, 649722, 2848524, 12441434, 54155774, 235008672, 1016971480, 4389589484, 18902538548, 81222609020, 348308661820, 1490884718484, 6370468593732, 27176620756392, 115760526170340, 492386739902574, 2091554077819948, 8873225318953248
Offset: 0
-
Table[Sum[Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, k}] * Binomial[2*n, n-k], {k, 0, n}], {n, 0, 30}]
A356290
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
Original entry on oeis.org
1, 5, 31, 200, 1309, 8627, 57082, 378648, 2516111, 16740913, 111494801, 743137984, 4956359312, 33074272702, 220810039566, 1474764797488, 9853307017341, 65853733243281, 440255398634199, 2944041287677060, 19691951641479427, 131744163990056479, 881586559906575688
Offset: 0
-
Table[Sum[Sum[PartitionsP[k-j]*PartitionsQ[j], {j, 0, k}] * Binomial[3*n, n-k], {k, 0, n}], {n, 0, 30}]
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