A084149 - OEIS

%I #20 Oct 13 2022 15:13:28

%S 1,9,1225,1656369,44604646326241,99356606870240615081050533361,

%T 198013920418138539775713504657052494285395323276110397576890625

%N Denominators of terms in the Pippenger product.

%H G. C. Greubel, <a href="/A084149/b084149.txt">Table of n, a(n) for n = 1..10</a>

%H Nicholas Pippenger, <a href="https://www.jstor.org/stable/2321215">An infinite product for e</a>, The American Mathematical Monthly, Vol. 87, No. 5 (1980), p. 391.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PippengerProduct.html">Pippenger Product</a>.

%F a(n) =  denominator(((2^(n-1)-1)!!*(2^n)!!/((2^(n-1))!!*(2^n-1)!!))^2/2). - _Amiram Eldar_, Apr 10 2022

%F a(n) = denominator( 2^(2^n -1)*((2^(n-1))!)^6 / (((2^n)!)^2 * ((2^(n-2))!)^4) ), with a(1) = 1. - _G. C. Greubel_, Oct 13 2022

%t a[n_] := Denominator[((2^(n - 1) - 1)!!*(2^n)!!/((2^(n - 1))!!*(2^n - 1)!!))^2/2]; Array[a, 7] (* _Amiram Eldar_, Apr 10 2022 *)

%o (Magma)

%o F:=Factorial;

%o A084149:= func< n | n eq 1 select 1 else Round(Denominator( 2^(2^n -1)*(F(2^(n-1)))^6 / ((F(2^n))^2 * (F(2^(n-2)))^4) )) >;

%o [A084149(n): n in [1..10]]; // _G. C. Greubel_, Oct 13 2022

%o (SageMath)

%o f=factorial

%o def A084149(n): return 1 if (n==1) else denominator( 2^(2^n -1)*(f(2^(n-1)))^6 / ((f(2^n))^2 * (f(2^(n-2)))^4) )

%o [A084149(n) for n in range(1,10)] # _G. C. Greubel_, Oct 13 2022

%Y Cf. A084148 (numerators).

%K frac,nonn

%O 1,2

%A _Eric W. Weisstein_, May 15 2003