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URL: https://oeis.org/A388528

⇱ A388528 - OEIS

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A388528
Decimal expansion of 81*Pi*sqrt(110 + 50*sqrt(5))/(5120*Gamma(7/4)^4).
2
1, 0, 3, 7, 4, 5, 3, 8, 6, 6, 3, 8, 1, 9, 9, 4, 6, 4, 5, 5, 3, 2, 8, 3, 8, 5, 9, 8, 4, 3, 0, 4, 9, 5, 5, 7, 9, 8, 9, 8, 5, 2, 4, 8, 3, 6, 8, 7, 1, 8, 9, 8, 8, 3, 5, 1, 7, 0, 4, 1, 2, 1, 0, 0, 6, 4, 7, 5, 4, 1, 3, 1, 2, 8, 2, 7, 8, 8, 7, 1, 7, 3, 8, 5, 6, 7, 9
OFFSET
1,3
LINKS
Simon Plouffe, Numbers in the base e^Pi, 2025.
FORMULA
Equals (1/1250) * Pi * 2^(2/5) * Gamma(9/10)^2 * Gamma(7/10)^2 * (1/4*5^(1/2)-1/4)^2 * (1/4*5^(1/2)+1/4)^2 * (5^(1/2) * sqrt(2) * (5+5^(1/2))^(1/2))^(11/2) / (sqrt(2) * 5^(1/2) * (5-5^(1/2))^(1/2))^(3/2) / Gamma(3/4)^4 / Gamma(4/5)^4.
Empirical: Equals Sum_{k>=0} A113185(k) / exp(k*Pi).
EXAMPLE
1.0374538663819946455328385984304955798...
MATHEMATICA
First[RealDigits[81*Pi*Sqrt[110 + 50*Sqrt[5]]/(5120*Gamma[7/4]^4), 10, 100]] (* Paolo Xausa, Sep 18 2025 *)
PROG
(PARI) (1/1250) * Pi * 2^(2/5) * gamma(9/10)^2 * gamma(7/10)^2 * (1/4*5^(1/2)-1/4)^2 * (1/4*5^(1/2)+1/4)^2 * (5^(1/2) * sqrt(2) * (5+5^(1/2))^(1/2))^(11/2) / (2^(1/2) * 5^(1/2) * (5-5^(1/2))^(1/2))^(3/2) / gamma(3/4)^4 / gamma(4/5)^4
CROSSREFS
Cf. A113185.
Sequence in context: A278389 A378975 A021271 * A238274 A388662 A094689
KEYWORD
nonn,cons
AUTHOR
Simon Plouffe, Sep 17 2025
STATUS
approved