Accelerate nested sum

I have a expression that is shown below. Basically all tables like mxTable, bTable and bulkTable have been pre-calculated.

enter image description here

The original expression looks like: enter image description here

Here are the definitions of tables:

quantity[n1_, n2_, n3_, n4_] :=    quantity[n3, n4, n1, n2] =     quantity[n1, n4, n3, n2] =      quantity[n3, n2, n1, n4] = mxtable[[n1, n2, n3, n4]]*\!\( \*UnderoverscriptBox[\(\[Sum]\), \(m1 = 0\), \(n1 - 1\)]\( \*UnderoverscriptBox[\(\[Sum]\), \(m2 = 0\), \(n2 - 1\)]\( \*UnderoverscriptBox[\(\[Sum]\), \(m3 = 0\), \(n3 - 1\)]\( \*UnderoverscriptBox[\(\[Sum]\), \(m4 = 0\), \(n4 -              1\)]\((bTable[\([n1 + 2, m1 + 3]\)] bTable[\([n2 + 2,                m2 + 3]\)] bTable[\([n3 + 2,                m3 + 3]\)] bTable[\([n4 + 2, m4 + 3]\)] bulk[\([m1 + 1,                m2 + 1, m3 + 1, m4 + 1]\)])\)\)\)\)\);    mxTable =    Table[1.0/     Sqrt[n1 (n1 + 1) n2 (n2 + 1) n3 (n3 + 1) n4 (n4 + 1)], {n1, 1,      50}, {n2, 1, 50}, {n3, 1, 50}, {n4, 1, 50}];  bTable = Table[Binomial[a, b], {a, 0, 250}, {b, 0, 250}];  ratioTable = Table[N[(m24 + 1)/2^(m13 + 3), 300] (-1)^(m13 + m24) (\!\( \*UnderoverscriptBox[\(\(\[Sum]\)\(\ \ \)\), \(k = 0\), \(m24 +           1\)] \(( \*FractionBox[\(1\), \(12\)] N[ \*FractionBox[\(Binomial[m13 + k + 4, k + 4]\),  SuperscriptBox[\(2\), \(k\)]],            300] \((k + 4)\) \((k + 3)\) \((k + 2)\) \((k +             1)\))\)\) + \!\( \*UnderoverscriptBox[\(\(\[Sum]\)\(\ \ \)\), \(l = 0\), \(m24 +           3\)] \((N[ \*FractionBox[\(Binomial[m13 + l + 2, l + 2]\),  SuperscriptBox[\(2\), \(l\)]],            300] \((l + 2)\) \((l + 1)\) \((m24 + 3)\) \((m24 +             2)\))\)\)), {m13, 0, 100}, {m24, 0, 100}];  bulkTable = Table[    bTable[[m1 + m3 + 1, m1 + 1]] bTable[[m2 + m4 + 1,        m2 + 1]] (ratioTable[[m1 + m3 + 1, m2 + m4 + 1]] +        ratioTable[[m2 + m4 + 1, m1 + m3 + 1]]), {m1, 0, 50}, {m2, 0,      50}, {m3, 0, 50}, {m4, 0, 50}]; 

Currently I would like to calculate a table of quantity with each argument from 1 to 50. i.e. a 50x50x50x50 table, but it takes a long time, partly because numbers in bTables are very large and also high precision is needed (with 300+ decimal places). Does anyone have a good idea how to accelerate the code, except for writing it in another language like cpp?