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

0,2

Links

Table of n, a(n) for n=0..12.

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A132317, A132318.

Sequence in context: A134245 A141313 A009144 * A136749 A226321 A054955

Adjacent sequences: A132313 A132314 A132315 * A132317 A132318 A132319

Keyword

nonn

Author

Paul D. Hanna, Aug 18 2007

Status

approved