Search: id:A014153
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%I A014153
%S A014153 1,3,7,14,26,45,75,120,187,284,423,618,890,1263,1771,2455,
%T A014153 3370,4582,6179,8266,10980,14486,18994,24757,32095,41391,
%U A014153 53123,67865,86325,109350,137979,173450,217270,271233,337506
%N A014153 G.f.: 1/[(1-x)^2*product((1-x^k),k=1..infinity)].
%C A014153 Number of partitions of n with three kinds of 1. E.g. a(2)=7 because 
               we have 2, 1+1, 1+1', 1+1", 1'+1', 1'+1", 1"+1". - Emeric Deutsch 
               (deutsch(AT)duke.poly.edu), Mar 22 2005
%C A014153 Partial sums of the partial sums of the partition numbers A000041. Partial 
               sums of A000070. Euler transform of 3,1,1,1,...
%C A014153 Also sum of parts, counted without multiplicity, in all partitions of 
               n, offset 1. Also Sum phi(p), where the sum is taken over all parts 
               p of all partitions of n, offset 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 26 2005
%C A014153 Equals row sums of triangle A141157. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 12 2008
%C A014153 A014153 convolved with A010815 = (1, 2, 3,...). n-th partial sum sequence 
               of A000041 convolved with A010815 = (n-1)-th column of Pascal's triangle, 
               starting (1, n,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Nov 09 2008]
%Y A014153 Cf. A000041.
%Y A014153 Cf. A000041, A000070.
%Y A014153 Cf. A141157.
%Y A014153 A010815 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 09 2008]
%Y A014153 Sequence in context: A051170 A008646 A036830 this_sequence A001924 A079921 
               A014168
%Y A014153 Adjacent sequences: A014150 A014151 A014152 this_sequence A014154 A014155 
               A014156
%K A014153 nonn
%O A014153 0,2
%A A014153 N. J. A. Sloane (njas(AT)research.att.com).

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