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%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
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