Search: id:A117086
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%I A117086
%S A117086 1,2,3,5,6,11,12,20,26,37,45,71,84,117,152,203,253,342,421,556,694,884,
%T A117086 1096,1409,1729,2168,2672,3327,4061,5039,6114,7514,9110,11098,13400,
%U A117086 16275,19537,23575,28245,33929,40465,48424,57552,68569,81296,96449
%N A117086 Number of partitions of n such that the largest part is a multiple of 
               the smallest part.
%C A117086 Also number of partitions of n such that the number of parts is a multiple 
               of the multiplicity of the largest part. Example: a(7)=12 because 
               from the 15 (=A000041(7)) partitions of 7 only [3,3,1], [2,2,2,1] 
               and [2,2,1,1,1] do not qualify (3,4,5 are not multiples of 2,3,2, 
               respectively). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 
               2006
%F A117086 G.f.: Sum(Sum(x^((l+1)*k)/Product(1-x^i,i=k..l*k),k=1..infinity),l=0..infinity).
%e A117086 a(7)=12 because from the 15 (=A000041(7)) partitions of 7 only [5,2],
               [4,3] and [3,2,2] do not qualify.
%p A117086 f:=add(add(x^((l+1)*k)/mul(1-x^i,i=k..l*k),k=1..51),l=0..51):s:=series(f,
               x,51):for m from 1 to 50 do c:=coeff(s,x,m):printf(`%d,`,c);od: (Jovovic) 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 2006
%Y A117086 Cf. A118096.
%Y A117086 Cf. A000041.
%Y A117086 Sequence in context: A033159 A083710 A127524 this_sequence A081026 A137808 
               A091909
%Y A117086 Adjacent sequences: A117083 A117084 A117085 this_sequence A117087 A117088 
               A117089
%K A117086 easy,nonn
%O A117086 1,2
%A A117086 Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 17 2006
%E A117086 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 21 2006

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