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Search: id:A046746
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| A046746 |
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Sum of smallest parts of all partitions of n. |
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+0
15
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| 0, 1, 3, 5, 9, 12, 20, 25, 38, 49, 69, 87, 123, 152, 205, 260, 341, 425, 555, 687, 882, 1094, 1380, 1702, 2140, 2620, 3254, 3982, 4907, 5967, 7318, 8856, 10787, 13019, 15759, 18943, 22840, 27334, 32794, 39139, 46758, 55595, 66182, 78433, 93021
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also total number of largest parts in all partitions of n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 16 2004
Starting with offset 1, = the partition triangle A026794 * [1, 2, 3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 13 2008
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FORMULA
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G.f.: sum_{k >= 1} (-1 + z^k/(1-z^k)(1-z^{k+1})(1-z^{k+2})...). - D. E. Knuth, Aug 08, 2002
G.f.: Sum_{k>=1} (-1+1/Product_{i>=0} (1-z^(k+i))) or Sum_{k>=1} k*z^k/Product_{i>=0} (1-z^(k+i)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 22 2003
G.f.: Sum(x^j/(1-x^j)/Product(1-x^i, i=1..j), j=1..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 11 2004
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CROSSREFS
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Cf. A006128.
Row sums of A026807.
Cf. A026794.
Sequence in context: A127722 A060419 A005766 this_sequence A058599 A059093 A084593
Adjacent sequences: A046743 A046744 A046745 this_sequence A046747 A046748 A046749
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KEYWORD
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nonn
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AUTHOR
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Dave Wilson
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