%I #7 Mar 24 2018 19:09:46

%S 1,0,0,1,0,1,0,0,2,0,1,1,0,3,0,2,2,0,5,0,2,4,0,7,1,3,7,0,10,2,4,11,0,

%T 14,4,5,17,0,19,8,6,25,1,25,13,8,36,2,33,21,10,50,4,43,33,12,69,8,55,

%U 49,15,93,14,70,71,19,124,23,88,102,24,163,37,110,142,31

%N Expansion of Product_{k>=1} (1 + x^(5*k))*(1 + x^(5*k-2)).

%C Number of partitions of n into distinct parts congruent to 0 or 3 mod 5.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: Product_{k>=2} (1 + x^A047218(k)).

%F a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(37/20) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 24 2018

%e a(13) = 3 because we have [13], [10, 3] and [8, 5].

%t nmax = 75; CoefficientList[Series[Product[(1 + x^(5 k)) (1 + x^(5 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 75; CoefficientList[Series[x^2 QPochhammer[-1, x^5] QPochhammer[-x^(-2), x^5]/(2 (1 + x^2)), {x, 0, nmax}], x]

%t nmax = 75; CoefficientList[Series[Product[(1 + Boole[MemberQ[{0, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A035369, A036822, A047218, A203776, A219607, A281271, A301562, A301563, A301564, A301565, A301567, A301568, A301570.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Mar 23 2018