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%I #4 Sep 24 2019 12:39:24
%S 1,1,3,6,16,35,85,195,465,1081,2549,5962,14016,32847,77119,180866,
%T 424466,995753,2336497,5481712,12861904,30176671,70802913,166120289,
%U 389761751,914476925,2145596677,5034105820,11811287658,27712248159,65019931641,152553127471,357928110743
%N Expansion of 1 / (1 - Sum_{i>=1, j>=0} x^(i*2^j)).
%C Invert transform of A001511.
%F G.f.: 1 / (1 - Sum_{k>=0} x^(2^k) / (1 - x^(2^k))).
%F a(0) = 1; a(n) = Sum_{k=1..n} A001511(k) * a(n-k).
%t nmax = 32; CoefficientList[Series[1/(1 - Sum[x^(2^k)/(1 - x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[IntegerExponent[2 k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 32}]
%Y Cf. A000041, A001511, A092119, A129921.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 23 2019
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