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A302836 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^(k^2)).

%I A302836 #6 Apr 13 2018 21:53:32
%S A302836 1,1,4,27,260,3150,46872,825944,16810048,387952668,10010010100,
%T A302836 285526191874,8921263237056,303013028232642,11116057874586840,
%U A302836 438023675344410000,18451248777413066768,827408674110381669305,39353155876513869320412,1978708139249503877752798
%N A302836 a(n) = [x^n] Product_{k>=1} 1/(1 - n*x^(k^2)).
%H A302836 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A302836 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A302836 a(n) ~ n^n * (1 + 1/n^3 + 1/n^6 + 1/n^8 + 1/n^9 + 1/n^11 + 1/n^12 + 1/n^14 + 2/n^15 + 1/n^16 + 1/n^17 + 2/n^18 + 1/n^19 + 1/n^20 + 2/n^21 + 1/n^22 + 2/n^23 + 4/n^24 + 1/n^25 + 2/n^26 + 4/n^27 + 1/n^28 + 2/n^29 + 5/n^30 + ...), for coefficients see A111178. - _Vaclav Kotesovec_, Apr 13 2018
%t A302836 Table[SeriesCoefficient[Product[1/(1 - n x^k^2), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
%Y A302836 Cf. A001156, A124577, A285245, A291583, A292417, A300974.
%K A302836 nonn
%O A302836 0,3
%A A302836 _Ilya Gutkovskiy_, Apr 13 2018