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Search: id:A116684
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| A116684 |
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Sum of the even parts in all partitions of n into distinct parts. |
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+0
3
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| 0, 0, 2, 2, 4, 6, 14, 18, 22, 34, 50, 66, 88, 118, 154, 202, 248, 320, 412, 512, 636, 794, 972, 1194, 1454, 1766, 2134, 2576, 3092, 3696, 4426, 5254, 6214, 7364, 8672, 10196, 11986, 14014, 16360, 19084, 22190, 25746, 29860, 34516, 39846, 45952, 52848
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=Sum(k*A116683(n,k), k>=0).
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FORMULA
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G.f.=2*product(1+x^j,j=1..infinity)*sum((jx^(2j)/(1+x^(2j)), j=1..infinity)).
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EXAMPLE
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a(9)=34 because in the partitions of 9 into distinct parts, namely, [9],[81],[72],[6,3],[6,2,1],[5,4],[5,3,1], and [4,3,2], the sum of the even parts is 8+2+6+6+2+4+4+2=34.
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MAPLE
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f:=2*product(1+x^j, j=1..60)*sum((j*x^(2*j)/(1+x^(2*j)), j=1..35)): fser:=series(f, x=0, 55): seq(coeff(fser, x, n), n=0..50);
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CROSSREFS
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Cf. A116681, A116682, A116683.
Adjacent sequences: A116681 A116682 A116683 this_sequence A116685 A116686 A116687
Sequence in context: A052953 A074028 A061894 this_sequence A116637 A134041 A069925
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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 22 2006
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