A084149 Denominators of terms in the Pippenger product.

1, 9, 1225, 1656369, 44604646326241, 99356606870240615081050533361, 198013920418138539775713504657052494285395323276110397576890625

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10

Nicholas Pippenger, An infinite product for e, The American Mathematical Monthly, Vol. 87, No. 5 (1980), p. 391.

Eric Weisstein's World of Mathematics, Pippenger Product.

Formula

a(n) = denominator(((2^(n-1)-1)!!*(2^n)!!/((2^(n-1))!!*(2^n-1)!!))^2/2). - Amiram Eldar, Apr 10 2022

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

Mathematica

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 *)

Prog

(Magma)
F:=Factorial;
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) )) >;
[A084149(n): n in [1..10]]; // G. C. Greubel, Oct 13 2022
(SageMath)
f=factorial
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) )
[A084149(n) for n in range(1, 10)] # G. C. Greubel, Oct 13 2022

Crossrefs

Cf. A084148 (numerators).

Sequence in context: A174253 A365595 A266602 * A202981 A276823 A020261

Adjacent sequences: A084146 A084147 A084148 * A084150 A084151 A084152

Keyword

frac,nonn

Author

Eric W. Weisstein, May 15 2003

Status

approved