Search: id:A067687
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%I A067687
%S A067687 1,1,2,5,12,29,69,165,393,937,2233,5322,12683,30227,72037,171680,409151,
%T A067687 975097,2323870,5538294,13198973,31456058,74966710,178662171,425791279,
%U A067687 1014754341,2418382956,5763538903,13735781840,32735391558,78015643589
%N A067687 Invert transform of right-shifted partition function (A000041).
%C A067687 Sums of the antidiagonals of the array formed by sequences A000007, A000041, 
               A000712, A000716, ... or its transpose A000012, A000027, A000096, 
               A006503, A006504, ....
%C A067687 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]
%C A067687 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]
%H A067687 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A067687 a(n) = Sum_{k=1..n} A000041(k-1)*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 07 2003
%e A067687 The array begins
%e A067687 1 1 1 1 1 1 1 1 ...
%e A067687 0 1 2 3 4 5 6 7 ...
%e A067687 0 2 5 9 14 20 27 ...
%e A067687 0 3 10 22 40 65 ...
%e A067687 0 5 20 51 105 ...
%e A067687 0 7 36 108 ...
%e A067687 0 11 65 ...
%o A067687 (From Joerg Arndt, May 08 2009) x='x+O('x^55) v=Vec( Ser( sum(n=0,33, 
               x^(n)/eta(x)^n ) ) )
%Y A067687 Cf. A000007, A000041, A000712, A000716, A000012, A000027, A000096, A006503, 
               A006504.
%Y A067687 Cf. table A060850.
%Y A067687 Cf, A137682, A143866.
%Y A067687 Sequence in context: A131045 A026721 A094975 this_sequence A130009 A048624 
               A000129
%Y A067687 Adjacent sequences: A067684 A067685 A067686 this_sequence A067688 A067689 
               A067690
%K A067687 nonn
%O A067687 0,3
%A A067687 Alford Arnold (Alford1940(AT)AOL.COM), Feb 05 2002
%E A067687 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 07 2003
%E A067687 More terms and better definition from Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Mar 14 2006

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