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Search: id:A116859
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| A116859 |
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Sum of the sizes of the Durfee squares of all partitions of n into distinct parts. |
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+0
2
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| 1, 1, 2, 2, 4, 6, 8, 10, 14, 18, 22, 29, 36, 46, 59, 72, 88, 110, 132, 160, 194, 232, 276, 330, 392, 464, 550, 648, 760, 894, 1044, 1216, 1418, 1644, 1905, 2204, 2540, 2924, 3364, 3859, 4420, 5060, 5778, 6590, 7514, 8544, 9706, 11018, 12484, 14130, 15980
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A116858(n,k),k>=1).
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FORMULA
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G.f.=sum(kx^(k(3k-1)/2)*(1+x^(2k))*product((1+x^j)/(1-x^j), j=1..k-1)/(1-x^k), k=1..infinity).
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EXAMPLE
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a(8)=10 because the partitions of 8 into distinct parts are [8],[7,1],[6,2],[5,3],[5,2,1], and [4,3,1], the sum of the sizes of their Durfee squares being 1+1+2+2+2+2=10.
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MAPLE
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f:=sum(k*x^(k*(3*k-1)/2)*(1+x^(2*k))*product((1+x^j)/(1-x^j), j=1..k-1)/(1-x^k), k=1..10): fser:=series(f, x=0, 60): seq(coeff(fser, x^n), n=1..55);
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CROSSREFS
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Cf. A116858.
Sequence in context: A118303 A145817 A145809 this_sequence A051466 A080015 A080054
Adjacent sequences: A116856 A116857 A116858 this_sequence A116860 A116861 A116862
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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), Feb 26 2006
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