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Search: id:A092314
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| A092314 |
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Sum of smallest parts of all partitions of n into odd parts. |
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+0
11
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| 1, 1, 4, 2, 7, 6, 11, 8, 18, 16, 24, 23, 34, 36, 51, 48, 66, 74, 90, 98, 126, 137, 164, 182, 220, 247, 294, 324, 380, 434, 496, 556, 650, 728, 835, 938, 1068, 1204, 1372, 1531, 1736, 1956, 2198, 2462, 2784, 3104, 3482, 3890, 4358, 4864, 5441, 6048, 6748, 7516
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=Sum(k*A116856(n,k),k>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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FORMULA
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G.f.: Sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k = n .. infinity), n = 1 .. infinity).
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EXAMPLE
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a(5)=7 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the smallest parts add up to 5+1+1=7.
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MAPLE
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g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k=n..30), n=1..30): gser:=series(g, x=0, 57): seq(coeff(gser, x^n), n=1..54); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 24 2006
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CROSSREFS
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Cf. A092322 A092269 A092309 A092321 A092313 A092310 A092311 A092268
Cf. A116856, A092322.
Sequence in context: A143370 A016695 A125271 this_sequence A110841 A128226 A049817
Adjacent sequences: A092311 A092312 A092313 this_sequence A092315 A092316 A092317
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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), Feb 15 2004
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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