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A261612 Expansion of Product_{k>=0} (1 + x^(3*k+1)).

%I A261612 #21 Nov 24 2020 02:23:17
%S A261612 1,1,0,0,1,1,0,1,1,0,1,2,1,1,2,1,1,3,2,1,3,3,2,4,4,2,4,5,3,5,7,4,5,8,
%T A261612 6,7,10,7,7,12,10,9,14,12,10,16,16,13,19,19,15,22,24,19,25,28,22,29,
%U A261612 35,28,33,40,33,38,48,41,44,55,48,51,66,59,58,74,69
%N A261612 Expansion of Product_{k>=0} (1 + x^(3*k+1)).
%H A261612 Vaclav Kotesovec, <a href="/A261612/b261612.txt">Table of n, a(n) for n = 0..10000</a>
%F A261612 a(n) ~ exp(Pi*sqrt(n)/3) / (2^(4/3) * sqrt(3) * n^(3/4)) * (1 - (Pi/144 + 9/(8*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Aug 26 2015, extended Jan 16 2017
%F A261612 G.f.: Sum_{k>=0} x^(k*(3*k - 1)/2) / Product_{j=1..k} (1 - x^(3*j)). - _Ilya Gutkovskiy_, Nov 24 2020
%t A261612 nmax = 100; CoefficientList[Series[Product[(1 + x^(3*k+1)), {k, 0, nmax}], {x, 0, nmax}], x]
%t A261612 nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[If[Mod[k, 3] == 1, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}];], {k, 2, nmax}]; poly (* _Vaclav Kotesovec_, Jan 13 2017 *)
%Y A261612 Cf. A000009, A000700, A035382, A169975.
%Y A261612 Cf. A015128, A080054, A261610, A261611, A262928.
%K A261612 nonn
%O A261612 0,12
%A A261612 _Vaclav Kotesovec_, Aug 26 2015