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URL: https://oeis.org/A256832

⇱ A256832 - OEIS

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A256832
Product of first n Pell numbers Pell(1), ... , Pell(n).
7
1, 2, 10, 120, 3480, 243600, 41168400, 16796707200, 16544756592000, 39343431175776000, 225870638380130016000, 3130567047948602021760000, 104751903991408172250111360000, 8462068308233934970708495883520000, 1650314871813323167662424409683488000000
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