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%I #9 May 10 2018 03:40:39
%S 0,0,1,1,1,1,2,3,3,3,5,7,7,8,12,15,16,19,24,30,34,39,49,60,67,77,95,
%T 112,127,147,175,206,234,267,315,367,415,474,553,637,720,820,945,1082,
%U 1223,1384,1585,1807,2032,2294,2612,2957,3321,3738,4229,4770,5344
%N Number of partitions of n into parts not of form 4k+2, 20k, 20k+1 or 20k-1. Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.
%C Case k=5,i=1 of Gordon/Goellnitz/Andrews Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.
%F a(n) ~ exp(Pi*sqrt(2*n/5)) * sin(Pi/20) / (10^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(20*k))*(1 - x^(20*k+1-20))*(1 - x^(20*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,7
%A _Olivier Gérard_
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