OFFSET
1,2
FORMULA
a(n) = Product_{k=1..n} A000129(k).
a(n) ~ c * ((1+sqrt(2))^(n*(n+1)/2) / 2^(3*n/2)), where c = A256831 = 1.1419825696677912... . - Vaclav Kotesovec, Apr 10 2015
MATHEMATICA
Table[Product[Expand[((1+Sqrt[2])^k-(1-Sqrt[2])^k)/(2*Sqrt[2])], {k, 1, n}], {n, 1, 20}]
FoldList[Times, LinearRecurrence[{2, 1}, {1, 2}, 20]] (* Harvey P. Dale, Oct 07 2015 *)
FoldList[Times, Fibonacci[Range[20], 2]] (* or *)
Table[Round[(1+Sqrt[2])^((n-1)n/2) QFactorial[n, Sqrt[8]-3]], {n, 20}] (* Vladimir Reshetnikov, Sep 15 2016 *)
PROG
(PARI) a(n)=my(q=quadgen(8)+1, Q=q); prod(k=2, n, imag(Q*=q)) \\ Charles R Greathouse IV, Feb 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 10 2015
STATUS
approved