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Search: id:A067687
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| A067687 |
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Invert transform of right-shifted partition function (A000041). |
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+0
3
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| 1, 1, 2, 5, 12, 29, 69, 165, 393, 937, 2233, 5322, 12683, 30227, 72037, 171680, 409151, 975097, 2323870, 5538294, 13198973, 31456058, 74966710, 178662171, 425791279, 1014754341, 2418382956, 5763538903, 13735781840, 32735391558, 78015643589
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Sums of the antidiagonals of the array formed by sequences A000007, A000041, A000712, A000716, ... or its transpose A000012, A000027, A000096, A006503, A006504, ....
Row sums of triangle A143866 = (1, 2, 5, 12, 29, 69, 165,...) and right border of A143866 = (1, 1, 2, 5, 12,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 04 2008]
Starting with offset 1 = A137682 / A000041; i.e. (1, 3, 7, 17, 40, 96,...) / (1, 2, 3, 5, 7, 11,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 01 2009]
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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a(n) = Sum_{k=1..n} A000041(k-1)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2003
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EXAMPLE
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The array begins
1 1 1 1 1 1 1 1 ...
0 1 2 3 4 5 6 7 ...
0 2 5 9 14 20 27 ...
0 3 10 22 40 65 ...
0 5 20 51 105 ...
0 7 36 108 ...
0 11 65 ...
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PROGRAM
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(From Joerg Arndt, May 08 2009) x='x+O('x^55) v=Vec( Ser( sum(n=0, 33, x^(n)/eta(x)^n ) ) )
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CROSSREFS
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Cf. A000007, A000041, A000712, A000716, A000012, A000027, A000096, A006503, A006504.
Cf. table A060850.
Cf, A137682, A143866.
Sequence in context: A131045 A026721 A094975 this_sequence A130009 A048624 A000129
Adjacent sequences: A067684 A067685 A067686 this_sequence A067688 A067689 A067690
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)AOL.COM), Feb 05 2002
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2003
More terms and better definition from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 14 2006
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