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%I #6 Oct 09 2020 02:51:07
%S 1,2,8,88,2812,284832,96344064,112162777984,458279216351168,
%T 6667184111642112512,349410072608155198029824,
%U 66605152356815910201401874432,46557942811582437260863430233248768
%N a(n) = [x^n] Product_{i=0..n} (1 + x^(2^i) )^(2^(n-i)).
%F a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Oct 09 2020
%e a(2) = [x^2] (1+x)^4*(1+x^2)^2*(1+x^4) = 8;
%e a(3) = [x^3] (1+x)^8*(1+x^2)^4*(1+x^4)^2*(1+x^8) = 88;
%e a(4) = [x^4] (1+x)^16*(1+x^2)^8*(1+x^4)^4*(1+x^8)^2*(1+x^16) = 2812.
%t Table[SeriesCoefficient[Product[(1 + x^(2^j))^(2^(n-j)),{j,0,n}],{x,0,n}], {n,0,15}] (* _Vaclav Kotesovec_, Oct 09 2020 *)
%o (PARI) {a(n)=polcoeff(prod(i=0,#binary(n),(1 + x^(2^i) +x*O(x^n))^(2^(n-i))), n)}
%Y Cf. A132317, A132318.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 18 2007
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