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Search: id:A096792
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| A096792 |
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Number of partitions of n into distinct parts with odd number of even parts. |
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+0
2
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| 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 9, 11, 13, 16, 19, 23, 27, 32, 38, 44, 52, 61, 71, 82, 96, 111, 128, 148, 170, 195, 224, 256, 292, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2049, 2291, 2560, 2859, 3189, 3554, 3959, 4404
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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a(n) = (A000009(n)-(-1)^n*A010815(n))/2.
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MATHEMATICA
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f[n_] := (PartitionsQ[n] + (-1)^(n + 1)* CoefficientList[ Series[ Product[(1 - x^k), {k, 1, 70}], {x, 0, 70}], x][[n + 1]])/2; Table[ f[n], {n, 0, 60}] (from Robert G. Wilson v Aug 27 2004)
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=x^n*O(x); polcoeff((eta(x^2+A)/eta(x+A) - eta(-x+A))/2, n)) /* Michael Somos, Aug 27 2004 */
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CROSSREFS
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Cf. A067659, A067661, A096791.
Sequence in context: A091493 A058724 A029021 this_sequence A015741 A015753 A005686
Adjacent sequences: A096789 A096790 A096791 this_sequence A096793 A096794 A096795
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 16 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Michael Somos, Aug 27 2004
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