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A084148 Numerators of terms in the Pippenger product. 2
2, 8, 1152, 1605632, 43913893117952, 98583626709555431615548620800, 197241992148713072661201501950348880945923403897735704916000768 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
From Amiram Eldar, Apr 10 2022: (Start)
a(n) = numerator(((2^(n-1)-1)!!*(2^n)!!/((2^(n-1))!!*(2^n-1)!!))^2/2).
Product_{n>=1} (a(n)/A084149(n))^(1/2^n) = e/2 (A019739). (End)
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
MATHEMATICA
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 *)
PROG
(Magma)
F:=Factorial;
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) )) >;
[A084148(n): n in [1..10]]; // G. C. Greubel, Oct 13 2022
(SageMath)
f=factorial
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) )
[A084148(n) for n in range(1, 10)] # G. C. Greubel, Oct 13 2022
CROSSREFS
Cf. A019739, A084149 (denominators).
Sequence in context: A322142 A061591 A103085 * A014115 A014116 A027668
KEYWORD
frac,nonn
AUTHOR
Eric W. Weisstein, May 15 2003
STATUS
approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)