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Search: id:A117955
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| A117955 |
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Number of partitions of n into exactly 2 types of odd parts. |
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+0
2
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| 0, 0, 0, 1, 1, 2, 3, 5, 4, 7, 8, 10, 11, 13, 12, 19, 18, 20, 22, 25, 24, 30, 31, 36, 33, 39, 38, 45, 45, 48, 51, 57, 54, 60, 56, 69, 67, 72, 72, 79, 78, 84, 84, 90, 87, 97, 97, 112, 99, 107, 112, 117, 115, 126, 118, 131, 134, 137, 136, 152, 143, 149, 149, 163, 152, 174, 164
(list; graph; listen)
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OFFSET
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1,6
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FORMULA
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G.f.=sum(sum(x^(2i+2j-2)/[(1-x^(2i-1))(1-x^(2j-1))], j=1..i-1), i=1..infinity).
G.f. for number of partitions of n into exactly m types of odd parts is obtained if we substitute x(i) with -Sum_{k>0}(x^(2*n-1)/(x^(2*n-1)-1))^i in the cycle index Z(S(m); x(1),x(2),..,x(m)) of the symmetric group S(m) of degree m. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 20 2007
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EXAMPLE
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a(8)=5 because we have [7,1],[5,3],[5,1,1,1],[3,3,1,1], and [3,3,1,1].
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MAPLE
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g:=sum(sum(x^(2*i+2*j-2)/(1-x^(2*i-1))/(1-x^(2*j-1)), j=1..i-1), i=1..40): gser:=series(g, x=0, 75): seq(coeff(gser, x^n), n=1..72);
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CROSSREFS
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Cf. A002133.
Sequence in context: A117120 A127515 A099424 this_sequence A074049 A127521 A102399
Adjacent sequences: A117952 A117953 A117954 this_sequence A117956 A117957 A117958
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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), Apr 05 2006
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