A046784 - OEIS

%I #9 Sep 16 2019 19:55:51

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,4,1,0,5,1,10,5,2,15,5,22,16,9,37,

%T 16,45,42,30,80,44,91,96,80,162,105,183,202,192,314,232,367,402,418,

%U 597,483,725,772,862,1115,966,1408,1445,1690,2066,1869,2672,2663,3209,3777

%N Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1, 2 and 4 (mod 5).

%H Andrew Howroyd, <a href="/A046784/b046784.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (Sum_{k>0} x^(12*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+3)). - _Andrew Howroyd_, Sep 16 2019

%o (PARI) seq(n)={Vec(sum(k=1, n\12, x^(12*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^(n-12*k)))^4)/prod(j=0, n\5, 1 - x^(5*j+3) + O(x*x^n)), -(n+1))} \\ _Andrew Howroyd_, Sep 16 2019

%Y Cf. A046787.

%K nonn

%O 0,18

%A _David W. Wilson_