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Search: id:A117276
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| A117276 |
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Number of 1's in all partitions of n with no even parts repeated. |
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+0
2
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| 0, 1, 2, 4, 7, 11, 17, 26, 38, 54, 76, 105, 143, 193, 257, 339, 444, 576, 742, 950, 1208, 1528, 1923, 2407, 2999, 3721, 4597, 5657, 6937, 8476, 10322, 12532, 15168, 18306, 22034, 26450, 31672, 37835, 45091, 53619, 63625, 75341, 89037, 105023, 123647
(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*A117274(n,k),k=0..n).
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FORMULA
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G.f.=x*product((1+x^(2j))/(1-x^(2j-1)), j=1..infinity)/(1-x).
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EXAMPLE
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a(5)=11 because the partitions of 5 with no even parts repeated are [5],[4,1],[3,2],[3,1,1],[2,1,1,1], and [1,1,1,1,1], and they have a total number 0+1+0+2+3+5=11 parts equal to 1.
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MAPLE
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g:=x*product((1+x^(2*j))/(1-x^(2*j-1)), j=1..35)/(1-x): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..47);
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CROSSREFS
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Cf. A117274.
Sequence in context: A004250 A084842 A096967 this_sequence A035295 A006999 A005252
Adjacent sequences: A117273 A117274 A117275 this_sequence A117277 A117278 A117279
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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 06 2006
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