%I #19 Oct 13 2022 15:28:06
%S 2,8,1152,1605632,43913893117952,98583626709555431615548620800,
%T 197241992148713072661201501950348880945923403897735704916000768
%N Numerators of terms in the Pippenger product.
%H G. C. Greubel, <a href="/A084148/b084148.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 From _Amiram Eldar_, Apr 10 2022: (Start)
%F a(n) = numerator(((2^(n-1)-1)!!*(2^n)!!/((2^(n-1))!!*(2^n-1)!!))^2/2).
%F Product_{n>=1} (a(n)/A084149(n))^(1/2^n) = e/2 (A019739). (End)
%F a(n) = numerator( 2^(2^n -1)*((2^(n-1))!)^6 / (((2^n)!)^2 * ((2^(n-2))!)^4) ), with a(1) = 2. - _G. C. Greubel_, Oct 13 2022
%t a[n_] := Numerator[((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 A084148:= func< n | n eq 1 select 2 else Round(Numerator( 2^(2^n -1)*(F(2^(n-1)))^6 / ((F(2^n))^2 * (F(2^(n-2)))^4) )) >;
%o [A084148(n): n in [1..10]]; // _G. C. Greubel_, Oct 13 2022
%o (SageMath)
%o f=factorial
%o def A084148(n): return 2 if (n==1) else numerator( 2^(2^n -1)*(f(2^(n-1)))^6 / ((f(2^n))^2 * (f(2^(n-2)))^4) )
%o [A084148(n) for n in range(1,10)] # _G. C. Greubel_, Oct 13 2022
%Y Cf. A019739, A084149 (denominators).
%K frac,nonn
%O 1,1
%A _Eric W. Weisstein_, May 15 2003