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Search: id:A027349
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| A027349 |
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Number of partitions of n into distinct odd parts, the least being 1. |
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+0
5
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| 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6, 8, 8, 9, 9, 11, 12, 13, 13, 16, 17, 18, 19, 22, 24, 25, 27, 30, 33, 35, 37, 41, 46, 47, 51, 56, 61, 64, 69, 75, 82, 86, 92, 100, 109, 114, 122, 133, 143, 151, 161, 174
(list; graph; listen)
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OFFSET
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1,13
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COMMENT
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Column 1 of A116860. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
Also number of partitions of n such that the largest part occurs exactly once and each number smaller than the largest part occurs an even nonzero number of times. Example: a(17)=3 because we have [3,2,2,2,2,2,2,1,1],[3,2,2,2,2,1,1,1,1,1,1] and [3,2,2,1,1,1,1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
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FORMULA
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G.f.=x*product(1+x^(2i-1), i=2..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
G.f.=sum(x^(k^2)/product(1-x^(2j), j=1..k-1), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 13 2006
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EXAMPLE
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a(17)=3 because we have [13,3,1],[11,5,1] and [9,7,1].
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MAPLE
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N := 100; t1 := series(mul(1+x^(2*k+1), k=1..N), x, N); A027349 := proc(n) coeff(t1, x, n); end;
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CROSSREFS
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Cf. A116860.
Sequence in context: A059169 A026922 A161090 this_sequence A053277 A078661 A029263
Adjacent sequences: A027346 A027347 A027348 this_sequence A027350 A027351 A027352
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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