A132317 a(n) = [x^(2^n)] Product_{i=0..n} (1 + x^(2^i) )^(2^(n-i)); equals column 1 of triangle A132318.

1, 2, 15, 1024, 7048181, 469389728563470, 2954306864416502250656677496683, 165756604793755389851497802171770083459242616940095659925793836

Offset: 0

Author

Paul D. Hanna, Aug 19 2007

Keywords

• nonn

Comments

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

Examples

			a(0) = [x] (1+x) = 1;
a(1) = [x^2] (1+x)^2*(1+x^2) = 2;
a(2) = [x^4] (1+x)^4*(1+x^2)^2*(1+x^4) = 15;
a(3) = [x^8] (1+x)^8*(1+x^2)^4*(1+x^4)^2*(1+x^8) = 1024;
a(4) = [x^16] (1+x)^16*(1+x^2)^8*(1+x^4)^4*(1+x^8)^2*(1+x^16) = 7048181.
		

Crossrefs

Cf. A132318, A132316.

Programs

Mathematica

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 *)

PARI

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