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Search: id:A117455
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| A117455 |
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Sum of the differences between the largest part and smallest part over all partitions of n into distinct parts. |
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+0
2
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| 0, 0, 1, 2, 4, 8, 12, 19, 27, 41, 54, 76, 99, 133, 171, 223, 279, 357, 443, 554, 682, 841, 1022, 1247, 1504, 1814, 2174, 2603, 3092, 3676, 4346, 5127, 6030, 7076, 8275, 9669, 11254, 13078, 15167, 17556, 20270, 23377, 26899, 30902, 35448, 40592, 46403
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)=sum(k*A117454(n,k),k=0..n-2).
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FORMULA
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G.f.=sum(x^(i(i+1)/2)*sum(1/(1-x^j), j=1..i-1)/product(1-x^j, j=1..i), i=1..infinity) (obtained by taking the derivative with respect to t of the g.f. G(t,x) of A117454 and letting t=1).
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EXAMPLE
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a(7)=12 because the partitions of 7 into distinct parts are [7],[6,1],[5,2],[4,3], and [4,2,1] and (7-7)+(6-1)+(5-2)+(4-3)+(4-1)=12.
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MAPLE
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g:=sum(x^(i*(i+1)/2)*sum(1/(1-x^j), j=1..i-1)/product(1-x^j, j=1..i), i=1..15): gser:=series(g, x=0, 55): seq(coeff(gser, x^n), n=1..50);
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CROSSREFS
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Cf. A117454.
Sequence in context: A125606 A136184 A011908 this_sequence A110571 A049696 A127405
Adjacent sequences: A117452 A117453 A117454 this_sequence A117456 A117457 A117458
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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 18 2006
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