Search: id:A089353
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%I A089353
%S A089353 1,2,1,3,2,1,4,6,2,1,5,10,6,2,1,6,19,14,6,2,1,7,28,28,14,6,2,1,8,44,52,
%T A089353 33,14,6,2,1,9,60,93,64,33,14,6,2,1,10,85,152,127,70,33,14,6,2,1,11,110,
%U A089353 242,228,142,70,33,14,6,2,1,12,146,370,404,272,149,70,33,14,6,2,1,13
%N A089353 Triangle read by rows: T(n,m) = number of planar partitions of n with 
               trace m.
%C A089353 Also number of partitions of n objects of 2 colors into k parts, each 
               part containing at least one black object.
%D A089353 G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (Ch. XI, 
               exercise 5 and Ch. XII, exercise 5).
%F A089353 G.f.: Prod(k=1..oo, 1/(1-q x^k)^k).
%e A089353 1; 2,1; 3,2,1; 4,6,2,1; 5,10,6,2,1; 6,19,14,6,2,1; ...
%Y A089353 Cf. A000219 (row sums), A005380, A005993 (trace 2), A050531 (trace 3), 
               A089351 (trace 4).
%Y A089353 Sequence in context: A029635 A104741 A167237 this_sequence A136451 A066121 
               A039911
%Y A089353 Adjacent sequences: A089350 A089351 A089352 this_sequence A089354 A089355 
               A089356
%K A089353 nonn,tabl
%O A089353 1,2
%A A089353 Wouter Meeussen and Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 26 2003
%E A089353 Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 08 2004

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