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Search: id:A052839
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| A052839 |
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Number of partitions of n into distinct summands (A000009), plus 1 (apart from the first term). |
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+0
3
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| 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 23, 28, 33, 39, 47, 55, 65, 77, 90, 105, 123, 143, 166, 193, 223, 257, 297, 341, 391, 449, 513, 586, 669, 761, 865, 983, 1114, 1261, 1427, 1611, 1817, 2049, 2305, 2591, 2911, 3265, 3659, 4098, 4583, 5121, 5719, 6379
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 806
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FORMULA
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G.f.: (-x-exp(Sum(-(-1)^(j[1]+1)*x^j[1]/(x^j[1]-1)/j[1], j[1]=1 .. infinity))+exp(Sum(-(-1)^(j[1]+1)*x^j[1]/(x^j[1]-1)/j[1], j[1]=1 .. infinity))*x)/(-1+x)
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MAPLE
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spec := [S, {C=Sequence(Z, 1 <= card), B=PowerSet(C), S=Union(B, C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..67);
Or: with(gfun, seriestolist); seriestolist(series(mul(1+z^i, i=1..81)+z/(1-z), z, 81));
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CROSSREFS
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Apart from the first term equals A000009 + 1 and also the left edge of A068049.
Sequence in context: A026798 A125890 A067661 this_sequence A125894 A091493 A058724
Adjacent sequences: A052836 A052837 A052838 this_sequence A052840 A052841 A052842
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Edited by Antti Karttunen, Feb 13 2002, based on information received from Bruno Salvy.
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