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Search: id:A116646
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| A116646 |
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Number of doubletons in all partitions of n. By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses). |
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3
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| 0, 0, 1, 0, 2, 2, 4, 5, 10, 11, 20, 25, 38, 49, 73, 91, 131, 167, 228, 291, 392, 493, 653, 822, 1065, 1336, 1714, 2131, 2706, 3354, 4209, 5193, 6471, 7934, 9817, 11990, 14725, 17909, 21875, 26477, 32172, 38797, 46893, 56339, 67804, 81147, 97260, 116017
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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a(n)=Sum(k*A116644(n,k), k>=0).
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FORMULA
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G.f.=x^2/[(1+x)(1-x^3)product(1-x^j, j=1..infinity)].
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EXAMPLE
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a(6)=4 because in the partitions of 6, namely [6],[5,1],[4,2],[4,(1,1)],[(3,3)],[3,2,1],[3,1,1,1],[2,2,2],[(2,2),(1,1)],[2,1,1,1,1], and [1,1,1,1,1,1], we have a total of 4 doubletons (shown between parentheses).
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MAPLE
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f:=x^2/(1+x)/(1-x^3)/product(1-x^j, j=1..70): fser:=series(f, x=0, 70): seq(coeff(fser, x, n), n=0..55);
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CROSSREFS
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Cf. A116644.
Sequence in context: A037026 A116651 A135586 this_sequence A091188 A127712 A032090
Adjacent sequences: A116643 A116644 A116645 this_sequence A116647 A116648 A116649
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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 20 2006
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