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Search: id:A117144
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| A117144 |
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Partitions of n in which each part k occurs at least k times. |
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+0
2
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| 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 8, 9, 10, 12, 15, 16, 19, 21, 25, 28, 32, 34, 41, 46, 51, 55, 64, 70, 79, 86, 97, 106, 119, 129, 146, 159, 175, 190, 214, 232, 256, 277, 306, 334, 367, 394, 434, 472, 515, 556, 607, 654, 714, 770, 836, 901, 978, 1048, 1140, 1226, 1322
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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G.f.=product((1-x^k+x^(k^2))/(1-x^k), k=1..infinity).
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EXAMPLE
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a(9)=5 because we have [3,3,3],[2,2,2,2,1],[2,2,2,1,1,1],[2,2,1,1,1,1,1], and [1,1,1,1,1,1,1,1,1].
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MAPLE
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g:=product((1-x^k+x^(k^2))/(1-x^k), k=1..100): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..66);
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CROSSREFS
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Cf. A052335.
Sequence in context: A113865 A143738 A029071 this_sequence A104408 A008718 A030719
Adjacent sequences: A117141 A117142 A117143 this_sequence A117145 A117146 A117147
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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), Mar 06 2006
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