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Decimal expansion of the coefficient of asymptotic expression of m(n), the number of multiplicative compositions of n.
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%I #17 Oct 16 2020 06:28:23

%S 3,1,8,1,7,3,6,5,2,2,0,9,0,5,6,8,7,4,3,7,6,4,4,9,1,6,7,2,7,5,6,8,4,7,

%T 1,0,4,5,1,3,5,1,9,8,5,4,4,9,2,9,0,9,5,3,2,3,8,9,3,1,1,5,3,7,2,5,9,3,

%U 5,3,9,3,6,2,3,0,6,7,7,4,6,6,9,0,9,7,0,0,6,7,4,6,3,4,0,0,6,0,5

%N Decimal expansion of the coefficient of asymptotic expression of m(n), the number of multiplicative compositions of n.

%C From _Amiram Eldar_, Oct 16 2020: (Start)

%C Equals -1/(rho * zeta'(rho)), where rho is the root of zeta(rho) = 2 (A107311).

%C Equals lim_{k->oo} A173382(k)/k^rho. (End)

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 293.

%e 0.318173652...

%t rho = x /. FindRoot[Zeta[x] == 2, {x, 2}, WorkingPrecision -> 100]; RealDigits[-1/(rho*Zeta'[rho])] // First

%o (PARI) a217598={my(rho=solve(x=1.1,2,zeta(x)-2));-1/(rho*zeta'(rho))} \\ _Hugo Pfoertner_, Oct 16 2020

%Y Cf. A074206, A107311 (rho), A173382.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Mar 19 2013