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A015723
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Number of parts in all partitions of n into distinct parts.
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11
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1, 1, 3, 3, 5, 8, 10, 13, 18, 25, 30, 40, 49, 63, 80, 98, 119, 149, 179, 218, 266, 318, 380, 455, 541, 640, 760, 895, 1050, 1234, 1442, 1679, 1960, 2272, 2635, 3052, 3520, 4054, 4669, 5359, 6142, 7035, 8037, 9170, 10460, 11896, 13517
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| Knopfmacher, Arnold and Robbins, Neville, Identities for the total number of parts in partitions of integers. Util. Math. 67 (2005), 9-18.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
| G.f.: Sum x^k/(1+x^k); k=1..inf * Product (1+x^m); m=1..inf. Convolution of A048272 and A000009. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 26 2002
G.f.: Sum_{k=1..inf} k*x^(k*(k+1)/2)/Product_{i=1..k}(1-x^i) . - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 21 2005
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CROSSREFS
| Cf. A006128, A079499, A067619, A186545.
Sequence in context: A105888 A123632 A039868 * A116645 A177739 A193744
Adjacent sequences: A015720 A015721 A015722 * A015724 A015725 A015726
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Extended and corrected by Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 24 2002
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