A132317 - OEIS

%I #5 Oct 09 2020 02:55:32

%S 1,2,15,1024,7048181,469389728563470,2954306864416502250656677496683,

%T 165756604793755389851497802171770083459242616940095659925793836

%N a(n) = [x^(2^n)] Product_{i=0..n} (1 + x^(2^i) )^(2^(n-i)); equals column 1 of triangle A132318.

%C Next term, a(8), has 126 digits.

%e a(0) = [x] (1+x) = 1;

%e a(1) = [x^2] (1+x)^2*(1+x^2) = 2;

%e a(2) = [x^4] (1+x)^4*(1+x^2)^2*(1+x^4) = 15;

%e a(3) = [x^8] (1+x)^8*(1+x^2)^4*(1+x^4)^2*(1+x^8) = 1024;

%e a(4) = [x^16] (1+x)^16*(1+x^2)^8*(1+x^4)^4*(1+x^8)^2*(1+x^16) = 7048181.

%t Table[SeriesCoefficient[Product[(1 + x^(2^j))^(2^(n-j)),{j,0,n}],{x,0,2^n}], {n,0,10}] (* _Vaclav Kotesovec_, Oct 09 2020 *)

%o (PARI) {a(n)=polcoeff(prod(i=0,n,(1 + x^(2^i) +x*O(x^(2^n)))^(2^(n-i))), 2^n)}

%Y Cf. A132318, A132316.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 19 2007