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A277210 Expansion of Product_{k>=1} 1/(1 - x^(3*k+1)). 2

%I

%S 1,0,0,0,1,0,0,1,1,0,1,1,1,1,2,1,2,2,2,2,4,3,3,4,5,4,6,6,7,7,9,8,11,

%T 11,12,13,16,15,18,20,22,22,27,27,31,33,37,38,45,46,51,55,62,63,72,76,

%U 84,89,99,103,116,122,133,142,158,164,181,193,210,222,245,257,281,299,324,343,376,396,429,457,495,522,568,601,649,689

%N Expansion of Product_{k>=1} 1/(1 - x^(3*k+1)).

%C Number of partitions of n into parts larger than 1 and congruent to 1 mod 3.

%C More generally, the ordinary generating function for the number of partitions of n into parts larger than 1 and congruent to 1 mod m (for m>0) is Product_{k>=1} 1/(1 - x^(m*k+1)).

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} 1/(1 - x^(3*k+1)).

%F a(n) ~ Pi^(1/3) * Gamma(1/3) * exp(sqrt(2*n)*Pi/3) / (2^(13/6)*3^(3/2)*n^(7/6)). - _Vaclav Kotesovec_, Oct 06 2016

%e a(14) = 2, because we have [10, 4] and [7, 7].

%t CoefficientList[Series[(1 - x)/QPochhammer[x, x^3], {x, 0, 85}], x]

%Y Cf. A016777, A035382, A087897, A117957.

%K nonn

%O 0,15

%A _Ilya Gutkovskiy_, Oct 05 2016

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Last modified February 22 09:44 EST 2018. Contains 299449 sequences. (Running on oeis4.)