A256832 - OEIS

%I #15 Feb 14 2022 22:43:36

%S 1,2,10,120,3480,243600,41168400,16796707200,16544756592000,

%T 39343431175776000,225870638380130016000,3130567047948602021760000,

%U 104751903991408172250111360000,8462068308233934970708495883520000,1650314871813323167662424409683488000000

%N Product of first n Pell numbers Pell(1), ... , Pell(n).

%F a(n) = Product_{k=1..n} A000129(k).

%F a(n) ~ c * ((1+sqrt(2))^(n*(n+1)/2) / 2^(3*n/2)), where c = A256831 = 1.1419825696677912... . - _Vaclav Kotesovec_, Apr 10 2015

%t Table[Product[Expand[((1+Sqrt[2])^k-(1-Sqrt[2])^k)/(2*Sqrt[2])],{k,1,n}],{n,1,20}]

%t FoldList[Times,LinearRecurrence[{2,1},{1,2},20]] (* _Harvey P. Dale_, Oct 07 2015 *)

%t FoldList[Times, Fibonacci[Range[20], 2]] (* or *)

%t Table[Round[(1+Sqrt[2])^((n-1)n/2) QFactorial[n, Sqrt[8]-3]], {n, 20}] (* _Vladimir Reshetnikov_, Sep 15 2016 *)

%o (PARI) a(n)=my(q=quadgen(8)+1,Q=q); prod(k=2,n, imag(Q*=q)) \\ _Charles R Greathouse IV_, Feb 14 2022

%Y Cf. A000129, A256831.

%Y Cf. A003266, A135407, A126772.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Apr 10 2015