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A277349 Expansion of Product_{k>=1} 1/(1 - x^(6*k+1)).

%I A277349 #10 Jan 23 2019 20:00:18
%S A277349 1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,1,2,1,1,0,0,1,2,2,
%T A277349 1,1,0,1,3,3,2,1,1,1,3,4,3,2,1,2,4,5,5,3,2,2,5,7,6,5,3,3,6,9,9,7,5,4,
%U A277349 7,11,12,10,7,6,9,14,16,14,11,8,11,17,20,19,15,12,14,21,26,25,21,17,18,26,32,33,28,23,24,32,41
%N A277349 Expansion of Product_{k>=1} 1/(1 - x^(6*k+1)).
%C A277349 Number of partitions of n into parts larger than 1 and congruent to 1 mod 6.
%H A277349 Robert Israel, <a href="/A277349/b277349.txt">Table of n, a(n) for n = 0..3000</a>
%H A277349 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A277349 G.f.: Product_{k>=1} 1/(1 - x^(6*k+1)).
%F A277349 a(n) ~ Pi^(1/6) * Gamma(1/6) * exp(sqrt(n)*Pi/3) / (24*sqrt(3)*n^(13/12)). - _Vaclav Kotesovec_, Oct 10 2016
%e A277349 a(26) = 2, because we have [19, 7] and [13, 13].
%p A277349 N:= 100:
%p A277349 G:= 1/mul(1-x^m,m=7..N,6):
%p A277349 S:= series(G,x,N+1):
%p A277349 seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Jan 23 2019
%t A277349 CoefficientList[Series[(1 - x)/QPochhammer[x, x^6], {x, 0, 100}], x]
%Y A277349 Cf. A016921, A087897, A109701 (partial sums), A117957, A277210, A277264.
%K A277349 nonn
%O A277349 0,27
%A A277349 _Ilya Gutkovskiy_, Oct 10 2016