code: def _d(n, j, prec, sq23pi, sqrt8):
      """
      Compute the sinh term in the outer sum of the HRR formula.
      The constants sqrt(2/3*pi) and sqrt(8) must be precomputed.
      """
      j = from_int(j)
      pi = mpf_pi(prec)
      a = mpf_div(sq23pi, j, prec)
      b = mpf_sub(from_int(n), from_rational(1, 24, prec), prec)
      c = mpf_sqrt(b, prec)
      ch, sh = mpf_cosh_sinh(mpf_mul(a, c), prec)
      D = mpf_div(
          mpf_sqrt(j, prec), mpf_mul(mpf_mul(sqrt8, b), pi), prec
      )
      E = mpf_sub(mpf_mul(a, ch), mpf_div(sh, c, prec), prec)
      return mpf_mul(D, E)
  
file_path: sympy/sympy/ntheory/partitions_.py
imports: from mpmath.libmp import fzero, from_int, from_rational, fone, fhalf, bitcount, to_int, to_str, mpf_mul, mpf_div, mpf_sub, mpf_add, mpf_sqrt, mpf_pi, mpf_cosh_sinh, mpf_cos, mpf_sin
  from sympy.external.gmpy import gcd, legendre, jacobi
  from .residue_ntheory import _sqrt_mod_prime_power, is_quad_residue
  import math
label_desc: Use image node_id 3 for calling a global function with example usage: _d(n, j, prec, sq23pi, sqrt8) and returns: mpf_mul