A132316 a(n) = [x^n] Product_{i=0..n} (1 + x^(2^i) )^(2^(n-i)).

1, 2, 8, 88, 2812, 284832, 96344064, 112162777984, 458279216351168, 6667184111642112512, 349410072608155198029824, 66605152356815910201401874432, 46557942811582437260863430233248768

Offset: 0

Author

Paul D. Hanna, Aug 18 2007

Keywords

• nonn

Examples

			a(2) = [x^2] (1+x)^4*(1+x^2)^2*(1+x^4) = 8;
a(3) = [x^3] (1+x)^8*(1+x^2)^4*(1+x^4)^2*(1+x^8) = 88;
a(4) = [x^4] (1+x)^16*(1+x^2)^8*(1+x^4)^4*(1+x^8)^2*(1+x^16) = 2812.
		

Crossrefs

Cf. A132317, A132318.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + x^(2^j))^(2^(n-j)),{j,0,n}],{x,0,n}], {n,0,15}] (* Vaclav Kotesovec, Oct 09 2020 *)

PARI

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

Formula

a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Oct 09 2020