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Search: id:A115584
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| A115584 |
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Number of partitions of n in which each part k occurs more than k times. |
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+0
1
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| 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 4, 3, 6, 4, 7, 7, 8, 8, 12, 9, 15, 14, 17, 18, 24, 21, 29, 29, 35, 35, 46, 42, 56, 54, 65, 67, 81, 77, 98, 95, 115, 114, 139, 135, 164, 165, 190, 195, 230, 225, 272, 271, 313, 321, 370, 374, 433, 441, 501, 514, 589, 592, 681, 698, 778, 809, 907
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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G.f.: Product((1-x^k+x^(k*(k+1)))/(1-x^k),k=1..infinity).
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EXAMPLE
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a(2)=1 because we have [1,1]; a(10)=4 because we have [2,2,2,2,2],[2,2,2,2,1,1],[2,2,2,1,1,1,1], and [1^10].
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MAPLE
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g:=product((1-x^k+x^(k*(k+1)))/(1-x^k), k=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=0..70); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 12 2006
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MATHEMATICA
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CoefficientList[ Series[ Product[(1 - x^k + x^(k(k + 1)))/(1 - x^k), {k, 14}], {x, 0, 66}], x] - Robert G. Wilson v (rgwv(at)rgwv.com)
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CROSSREFS
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Cf. A117144, A052335, A087153.
Adjacent sequences: A115581 A115582 A115583 this_sequence A115585 A115586 A115587
Sequence in context: A054685 A029141 A058742 this_sequence A029140 A008584 A034390
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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.yu), Mar 09 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 12 2006
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