**Bug introduced in 7.0 or earlier and persisting through 11.1 or later. Fixed in 11.3**

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I computed a following limit (related to the asymptotic expansion of the sequence [`A000009`](http://oeis.org/A000009) - number of partitions of `n` into distinct parts)

    Expand[Limit[(((π BesselI[1, (Sqrt[1/24 + n] π)/Sqrt[3]])/Sqrt[1 + 24 n])/
                 (E^((Sqrt[n] π)/Sqrt[3])/(4 3^(1/4) n^(3/4))) -
                 (1 + (-((3 Sqrt[3])/(8 π)) + π/(48 Sqrt[3]))/Sqrt[n] +
                  (-(5/128) - 45/(128 π^2) + π^2/13824)/n))*n^(3/2), n -> Infinity]]

*Mathematica* wrong output (in all versions from 7 to 11) is

    (* (35 Sqrt[3])/(2048 π) - (35 π)/(36864 Sqrt[3]) + π^3/(1990656 Sqrt[3]) *)
This expression is equal to

    (* 0.007709031447942101952246679 *)

But the correct result is

    (* -((315 Sqrt[3])/(1024 π^3)) + (35 Sqrt[3])/(2048 π) -
       (35 π)/(36864 Sqrt[3]) + π^3/(1990656 Sqrt[3]) *)
This is equal to

    (* -0.009474863397773687074232327 *)

My question is: why is the term

    (* -((315 Sqrt[3])/(1024 π^3)) *)

missing in the *Mathematica* result? This is a bug!

Interesting is that numerically *Mathematica* evaluates a following expression correctly:

    Table[N[(((π BesselI[1, (Sqrt[1/24 + n] π)/Sqrt[3]])/Sqrt[1 + 24 n])/
             (E^((Sqrt[n] π)/Sqrt[3])/(4 3^(1/4) n^(3/4))) -
             (1 + (-((3 Sqrt[3])/(8 π)) + π/(48 Sqrt[3]))/Sqrt[n] +
              (-(5/128) - 45/(128 π^2) + π^2/13824)/n))*n^(3/2), 10],
          {n, 1000000, 10000000, 1000000}]

    (* {-0.009484688338, -0.009481807906, -0.009480532562, -0.009479772520, -0.009479253935, -0.009478871178, -0.009478573728, -0.009478333979, -0.009478135403, -0.009477967422} *)

Maple evaluates this limit correctly. Here is the Maple code: 

    expand(simplify(limit((Pi * BesselI(1, Pi * sqrt((n+1/24) * (1/3)))*(4 * 3^(1/4) * n^(3/4))/(sqrt(24 * n+1)*exp(Pi * sqrt((1/3) * n)))-1-(Pi/(48 * sqrt(3))-3 * sqrt(3)/(8 * Pi))/sqrt(n)-((1/13824) * Pi^2-5/128-45/(128 * Pi^2))/n) * n^(3/2), n = infinity))); evalf(%, 60);