Search: id:A060184
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%I A060184
%S A060184 1,0,1,2,0,1,1,2,1,2,0,0,1,2,1,1,2,0,1,3,1,5,6,0,0,1,1,2,1,5,5,2,0,2,3,
               2,2,9,10,
%T A060184 0,1,4,3,0,4,0,2,9,9,3,1,3,2,7,2,0,3,14,16,0,2,6,1,9,2,0,3,15,17,2,1,8,
               19,10,6,
%U A060184 4,0,1,0,15,22,0,1,9,21,7,13,2,0,2,4,11,20,4,2,15,33,14,15,3,0,4,10,10,
               28,0,3
%V A060184 1,0,1,2,0,-1,1,2,1,2,0,0,1,2,1,1,-2,0,1,3,1,5,6,0,0,-1,-1,2,1,5,5,-2,
               0,-2,-3,2,2,9,10,
%W A060184 0,1,4,3,0,4,0,2,9,9,-3,1,3,-2,-7,2,0,3,14,16,0,2,6,-1,-9,2,0,3,15,17,
               -2,1,8,19,10,-6,
%X A060184 4,0,-1,0,15,22,0,1,9,21,7,-13,2,0,-2,-4,11,20,-4,2,15,33,14,-15,3,0,-4,
               -10,10,28,0,3
%N A060184 Triangle of generalized sum of divisors function, read by rows.
%C A060184 Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).
%D A060184 P. A. MacMahon, Divisors of numbers and their continuations in the theory 
               of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. 
               Papers II, pp. 303-341.
%F A060184 G.f. for k-th diagonal (the k-th row of the sideways triangle shown in 
               the example): Sum_{ m_1 < m_2 < ... < m_k} q^(m_1+m_2+...+m_k)/((1+q^m_1)*(1+q^m_2)*...*(1+q^m_k)) 
               = Sum_n T(n, k)*q^n.
%e A060184 Triangle turned on its side begins:
%e A060184 .1 0 2 -1 2 0 2 -2 3 .0 .2 etc
%e A060184 .... 1 .0 1 2 1 .1 1 .6 -1 etc
%e A060184 ......... 1 0 1 .0 5 -1 .5 etc
%Y A060184 Diagonals give A048272, A060185, A060186. Cf. A060043, A060044, A060047, 
               A060177.
%Y A060184 Sequence in context: A117468 A116374 A025911 this_sequence A055639 A156542 
               A066360
%Y A060184 Adjacent sequences: A060181 A060182 A060183 this_sequence A060185 A060186 
               A060187
%K A060184 sign,tabf,easy,nice
%O A060184 1,4
%A A060184 N. J. A. Sloane (njas(AT)research.att.com), Mar 20 2001
%E A060184 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 2007

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