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A067588
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Total number of parts in all partitions of n into odd parts.
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3
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0, 1, 2, 4, 6, 9, 14, 19, 26, 36, 48, 62, 82, 104, 132, 169, 210, 260, 324, 396, 484, 592, 714, 860, 1036, 1238, 1474, 1756, 2078, 2452, 2894, 3396, 3976, 4654, 5422, 6309, 7332, 8490, 9816, 11338, 13060, 15018, 17254, 19774, 22630, 25878, 29524, 33642
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Starting with "1" = triangle A097304 * [1, 2, 3,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2010]
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FORMULA
| G.f.: G(x)*H(x) where G(x) = Sum_{k>=1) x^(2*k-1)/(1-x^(2*k-1)) is g.f. for the number of odd divisors of n (cf. A001227) and H(x) = Product_{k>=1) (1+x^k) is g.f. for the number of partitions of n into odd parts (cf. A000009). Convolution of A001227 and A000009: Sum_{k=0..n} A001227(k)*A000009(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 04 2002
G.f.: Sum_{n>0} n*x^n/Product_{k=1..n} (1-x^(2*k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 15 2003
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CROSSREFS
| Cf. A067589, A006128, A066897, A066898.
Cf. A097304 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 09 2010]
Sequence in context: A113753 A024457 A117842 * A003402 A034748 A069916
Adjacent sequences: A067585 A067586 A067587 * A067589 A067590 A067591
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KEYWORD
| easy,nonn
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Jan 31 2002
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EXTENSIONS
| Corrected by James A. Sellers (sellersj(AT)math.psu.edu), May 31 2007
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