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Memory related problem, using ParallelTable[]

Posted 3 months ago
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I have the following code:

\[Alpha] = 10^6;
L = Total@*Map[Length];
\[DoubleStruckCapitalT][i_, j_] := Binomial[i, j - 1];
L[ParallelTable[
   If[TrueQ[
     EvenQ[\[DoubleStruckCapitalT][n, k]] && \[DoubleStruckCapitalT][
        n, k] != 0], {n, k}, Nothing], {n, 0, \[Alpha] - 1}, {k, 
    1, \[Alpha]}] //. {} -> Nothing]

But this code gives an error memory message, how can I edit my code such that I want to compute this code for large values of \[Alpha]?

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