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Search: id:A118082
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| A118082 |
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Number of partitions of n such that largest part k occurs floor(k/2) times. |
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3
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| 1, 0, 1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 12, 15, 19, 22, 27, 32, 39, 45, 54, 63, 75, 87, 102, 118, 139, 160, 186, 214, 248, 284, 328, 375, 430, 490, 561, 637, 727, 824, 935, 1058, 1199, 1352, 1528, 1720, 1938, 2177, 2448, 2743, 3079, 3445, 3856, 4307, 4813, 5365, 5985
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also number of partitions of n such that if the number of parts is k, then the smallest part is floor(k/2). Example: a(8)=5 because we have [7,1],[6,1,1],[5,2,1],[4,3,1], and [2,2,2,2].
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FORMULA
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G.f.=sum(x^(k*floor(k/2))/product(1-x^j, j=1..k-1), k=1..infinity).
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EXAMPLE
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a(8)=5 because we have [4,4],[3,2,2,1],[3,2,1,1,1],[3,1,1,1,1,1], and [2,1,1,1,1,1,1].
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MAPLE
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g:=sum(x^(k*floor(k/2))/product(1-x^j, j=1..k-1), k=1..15): gser:=series(g, x=0, 65): seq(coeff(gser, x, n), n=0..60);
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CROSSREFS
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Cf. A118083, A118084.
Sequence in context: A015741 A015753 A005686 this_sequence A120160 A017980 A064650
Adjacent sequences: A118079 A118080 A118081 this_sequence A118083 A118084 A118085
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 12 2006
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