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Search: id:A103650
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| A103650 |
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G.f.: x^2/((1-x^2)^2*Product_{i>0}(1-x^i)). |
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+0
1
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| 0, 1, 1, 4, 5, 12, 16, 31, 42, 72, 98, 155, 210, 315, 423, 610, 812, 1136, 1498, 2047, 2674, 3585, 4642, 6125, 7865, 10240, 13046, 16791, 21237, 27060, 33993, 42933, 53591, 67155, 83332, 103687, 127956, 158196, 194217, 238720, 291663, 356582
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Let pi be a partition of n and b(pi,k) = Sum p, where p runs over all distinct parts p of pi whose multiplicities are >=k. Let T(n,k) = Sum b(pi,k), when pi runs over all partitions pi of n. G.f. for T(n,k) is x^k/((1-x^k)^2*Product_{i>0}(1-x^i)). a(n) = T(n,2).
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EXAMPLE
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Partitions of 4 are [1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4] and a(4) = 1 + 1 + 2 + 0 + 0 = 4.
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MATHEMATICA
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Drop[ CoefficientList[ Series[ x^2/((1 - x^2)^2*Product[(1 - x^i), {i, 50}]), {x, 0, 42}], x], 1] (from Robert G. Wilson v Mar 29 2005)
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CROSSREFS
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Cf. A014153.
Sequence in context: A050022 A137619 A115375 this_sequence A131116 A131328 A054451
Adjacent sequences: A103647 A103648 A103649 this_sequence A103651 A103652 A103653
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 26 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 29 2005
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