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%I #21 May 10 2018 23:07:44
%S 1,1,2,3,5,7,11,15,22,30,41,54,74,96,127,164,213,271,348,438,555,694,
%T 869,1077,1339,1647,2029,2482,3036,3690,4487,5423,6555,7886,9480,
%U 11350,13583,16191,19287,22902,27169,32138,37984,44772,52726,61948
%N Number of partitions of n into parts not of the form 21k, 21k+10 or 21k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 9 are greater than 1.
%C Case k=10,i=10 of Gordon Theorem.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
%H Seiichi Manyama, <a href="/A035988/b035988.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Andrews-GordonIdentity.html">Andrews-Gordon Identity</a>
%F a(n) ~ exp(2*Pi*sqrt(n/7)) * cos(Pi/42) / (sqrt(3) * 7^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
%t nmax = 60; CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+10-21))*(1 - x^(21*k-10))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 10 2018 *)
%K nonn,easy
%O 0,3
%A _Olivier Gérard_
%E a(0)=1 prepended by _Seiichi Manyama_, May 10 2018