%I #9 Aug 20 2018 07:51:45
%S 1,2,4,8,17,38,86,192,420,905,1939,4163,8987,19494,42368,91990,199127,
%T 429345,921982,1972553,4206909,8949412,19001874,40293048,85373962,
%U 180826115,382957231,811027414,1717497958,3636335170,7695599294,16275268520,34389570596
%N Binomial transform of A001156.
%H Vaclav Kotesovec, <a href="/A294529/b294529.txt">Table of n, a(n) for n = 0..3000</a>
%F a(n) = Sum_{k=0..n} binomial(n,k) * A001156(k).
%F a(n) ~ exp(3 * 2^(-5/3) * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3)) * Zeta(3/2)^(2/3) * 2^(n - 7/6) / (sqrt(3) * Pi^(7/6) * n^(7/6)).
%F G.f.: (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k^2)/(1 - x)^(k^2)). - _Ilya Gutkovskiy_, Aug 20 2018
%t nmax = 40; s = CoefficientList[Series[Product[1/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]
%Y Cf. A001156, A218481, A266232, A294500, A294530.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 02 2017