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A202088 Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).

%I A202088 #11 Sep 16 2019 22:02:03
%S A202088 0,0,1,4,11,25,55,116,245,505,1026,2030,3936,7450,13837,25210,45206,
%T A202088 79831,139136,239471,407582,686346,1144532,1890837,3096692,5029412,
%U A202088 8104448,12961576,20582130,32459992,50859769,79192204,122572743
%N A202088 Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).
%C A202088 For a given partition, cn(i,n) means the number of its parts equal to i modulo n.
%H A202088 Andrew Howroyd, <a href="/A202088/b202088.txt">Table of n, a(n) for n = 0..1000</a>
%H A202088 <a href="/wiki/Partitions_of_5n">Index and properties of sequences related to partitions of 5n</a>
%F A202088 a(n) = A036888(n) - A036893(n).
%F A202088 a(n) = A202087(n) - A046776(n).
%F A202088 G.f.: Sum_{k>=0} x^(2*k)*(1-x^k)/(Product_{j=1..k} 1 - x^j)^5. - _Andrew Howroyd_, Sep 16 2019
%o A202088 (PARI) seq(n)={Vec(sum(k=0, n\2, x^(2*k)*(1-x^k)/prod(j=1, k, 1 - x^j + O(x*x^n))^5) + O(x*x^n), -(n+1))} \\ _Andrew Howroyd_, Sep 16 2019
%Y A202088 Cf. A036888, A036893, A046776, A202087.
%K A202088 nonn
%O A202088 0,4
%A A202088 _Max Alekseyev_, Dec 11 2011
%E A202088 a(0)=0 prepended by _Andrew Howroyd_, Sep 16 2019