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A026804
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Number of partitions of n in which the least part is odd.
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6
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1, 1, 3, 3, 6, 8, 13, 16, 25, 33, 47, 61, 84, 109, 148, 189, 249, 319, 413, 522, 670, 842, 1066, 1330, 1668, 2068, 2574, 3171, 3915, 4800, 5888, 7175, 8753, 10617, 12879, 15552, 18772, 22570, 27125, 32480, 38867, 46372, 55275
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Also number of partitions of n in which the largest part occurs an odd number of times. Example: a(5)=6 because we have [5],[4,1],[3,2],[3,1,1],[2,1,1,1] and [1,1,1,1,1] ([2,2,1] does not qualify). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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FORMULA
| G.f.: Sum_{k>=1} ((-1)^(k+1)*(-1+1/Product_{i>=k} (1-x^i))). a(n) = Sum_{k=1..n} (-1)^(k+1)*A026807(n, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 26 2003
G.f.: Sum(x^j/(1+x^j)/Product(1-x^i, i=1..j), j=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 11 2004
G.f.=sum(x^(2k-1)/product(1-x^j,j=2k-1..infinity),k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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EXAMPLE
| a(5)=6 because we have [5],[4,1],[3,1,1],[2,2,1],[2,1,1,1] and [1,1,1,1,1] ([3,2] does not qualify).
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MAPLE
| g:=sum(x^(2*k-1)/product(1-x^j, j=2*k-1..50), k=1..50): gser:=series(g, x=0, 45): seq(coeff(gser, x, n), n=1..43); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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CROSSREFS
| Cf. A046746.
Sequence in context: A174524 A143592 A097307 * A205970 A104715 A164743
Adjacent sequences: A026801 A026802 A026803 * A026805 A026806 A026807
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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