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A309677 G.f. A(x) satisfies: A(x) = A(x^3) / (1 - x)^2.

%I A309677 #12 Aug 15 2019 18:05:36
%S A309677 1,2,3,6,9,12,18,24,30,42,54,66,87,108,129,162,195,228,279,330,381,
%T A309677 456,531,606,711,816,921,1068,1215,1362,1563,1764,1965,2232,2499,2766,
%U A309677 3120,3474,3828,4290,4752,5214,5805,6396,6987,7740,8493,9246,10194,11142
%N A309677 G.f. A(x) satisfies: A(x) = A(x^3) / (1 - x)^2.
%C A309677 Self-convolution of A062051.
%H A309677 Alois P. Heinz, <a href="/A309677/b309677.txt">Table of n, a(n) for n = 0..10000</a>
%F A309677 G.f.: Product_{k>=0} 1/(1 - x^(3^k))^2.
%p A309677 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
%p A309677       b(n, i-1)+(p-> `if`(p>n, 0, b(n-p, i)))(3^i)))
%p A309677     end:
%p A309677 a:= n-> add(b(j, ilog[3](j))*b(n-j, ilog[3](n-j)), j=0..n):
%p A309677 seq(a(n), n=0..52);  # _Alois P. Heinz_, Aug 12 2019
%t A309677 nmax = 52; A[_] = 1; Do[A[x_] = A[x^3]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A309677 nmax = 52; CoefficientList[Series[Product[1/(1 - x^(3^k))^2, {k, 0, Floor[Log[3, nmax]] + 1}], {x, 0, nmax}], x]
%Y A309677 Cf. A005704, A062051, A120880, A171238, A309678, A309679.
%K A309677 nonn
%O A309677 0,2
%A A309677 _Ilya Gutkovskiy_, Aug 12 2019