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Search: id:A118199
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| A118199 |
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Number of partitions of n having no parts equal to the size of their Durfee squares. |
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+0
2
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| 1, 0, 1, 1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 40, 53, 68, 89, 113, 146, 184, 234, 293, 369, 458, 572, 706, 874, 1073, 1320, 1611, 1970, 2393, 2909, 3518, 4255, 5122, 6167, 7394, 8862, 10585, 12637, 15038, 17886, 21213, 25141, 29723, 35112, 41383, 48737, 57278
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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a(n)=A118198(n,0).
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FORMULA
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G.f.=1+sum(x^(k^2+k)/[(1-x^k)*product((1-x^i)^2, i=1..k-1)], k=1..infinity).
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EXAMPLE
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a(7)=3 because we have [7] with size of Durfee square 1, [4,3] with size of Durfee square 2, and [3,3,1] with size of Durfee square 2.
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MAPLE
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g:=1+sum(x^(k^2+k)/(1-x^k)/product((1-x^i)^2, i=1..k-1), k=1..20): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..54);
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CROSSREFS
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Cf. A118198, A000041.
Sequence in context: A001401 A008628 A038499 this_sequence A088318 A038083 A060688
Adjacent sequences: A118196 A118197 A118198 this_sequence A118200 A118201 A118202
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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 14 2006
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