A256832 Product of first n Pell numbers Pell(1), ... , Pell(n).

1, 2, 10, 120, 3480, 243600, 41168400, 16796707200, 16544756592000, 39343431175776000, 225870638380130016000, 3130567047948602021760000, 104751903991408172250111360000, 8462068308233934970708495883520000, 1650314871813323167662424409683488000000

Offset: 1

Author

Vaclav Kotesovec, Apr 10 2015

Keywords

• nonn

Crossrefs

Cf. A000129, A256831.

Cf. A003266, A135407, A126772.

Programs

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 *)

PARI

a(n)=my(q=quadgen(8)+1,Q=q); prod(k=2,n, imag(Q*=q)) \\ Charles R Greathouse IV, Feb 14 2022

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