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A086543
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Number of partitions of n with at least one odd part.
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2
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0, 1, 1, 3, 3, 7, 8, 15, 17, 30, 35, 56, 66, 101, 120, 176, 209, 297, 355, 490, 585, 792, 946, 1255, 1498, 1958, 2335, 3010, 3583, 4565, 5428, 6842, 8118, 10143, 12013, 14883, 17592, 21637, 25525, 31185, 36711, 44583, 52382, 63261, 74173, 89134
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| A000041(n) if n is odd else A000041(n)-A000041(n/2).
G.f.=sum(x^(2k-1)/[product(1-x^j, j=1..2k-1)*product(1-x^(2j), j=k..infinity)], k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
| a(4)=3 because we have [3,1],[2,1,1] and [1,1,1] ([4] and [2,2] do not qualify).
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MAPLE
| g:=sum(x^(2*k-1)/product(1-x^j, j=1..2*k-1)/product(1-x^(2*j), j=k..70), k=1..70): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..45); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
| Cf. A038348, A047967.
Sequence in context: A200792 A161416 A117989 * A110618 A108046 A116157
Adjacent sequences: A086540 A086541 A086542 * A086544 A086545 A086546
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 10 2003
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