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%I #8 May 10 2018 03:13:56
%S 1,2,3,5,7,10,14,20,27,37,49,66,85,112,144,186,236,301,378,477,594,
%T 741,916,1134,1391,1708,2083,2540,3079,3732,4500,5424,6508,7803,9321,
%U 11125,13231,15723,18628,22048,26024,30688,36097,42419,49736,58254
%N Number of partitions of n into parts not of the form 19k, 19k+6 or 19k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 8 are greater than 1.
%C Case k=9,i=6 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%F a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(7*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 6-19))*(1 - x^(19*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 1,2
%A _Olivier Gérard_
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