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%I #26 Feb 12 2023 15:19:26
%S 1,2,1,3,6,1,4,12,6,12,1,5,20,20,30,30,20,1,6,30,30,60,15,120,60,20,
%T 90,30,1,7,42,42,105,42,210,140,105,105,420,105,140,210,42,1,8,56,56,
%U 168,56,336,280,28,336,168,840,280,168,420,840,1120,168,70,560,420,56,1
%N Triangle of multiplicities of k-th partition of n corresponding to sequence A080577. Multiplicity of a given partition of n into k parts is the number of ways parts can be selected from k distinguishable bins. See the example.
%C Differs from A035206 after position 21.
%C Differs from A210238 after position 21.
%H Sergei Viznyuk, <a href="http://phystech.com/ftp/s_A209936.c">C Program</a>
%e 1
%e 2, 1
%e 3, 6, 1
%e 4, 12, 6, 12, 1
%e 5, 20, 20, 30, 30, 20, 1
%e 6, 30, 30, 60, 15, 120, 60, 20, 90, 30, 1
%e 7, 42, 42, 105, 42, 210, 140, 105, 105, 420, 105, 140, 210, 42, 1
%e Thus for n=3 (third row) the partitions of n=3 are
%e 3+0+0 0+3+0 0+0+3 (multiplicity=3)
%e 2+1+0 2+0+1 1+2+0 1+0+2 0+2+1 0+1+2 (multiplicity=6)
%e 1+1+1 (multiplicity=1)
%Y Cf. A080577, A078760, A035206, A210238.
%Y Row lengths give A000041.
%Y Row sums give A088218.
%K nonn,tabf
%O 1,2
%A _Sergei Viznyuk_, Mar 15 2012
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