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Sum Holonomic Sequences
The sum of a holonomic sequence is always holonomic.
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DifferenceRootReduce[(n/2)!^3, n]
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In[2]:=

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DifferenceRootReduce[(n/2)!^3, n];

Sum[%, n]
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In[3]:=

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DifferenceRootReduce[(n/2)!^3, n];

Sum[%, n];

DifferenceRootReduce[DifferenceDelta[%, n] - (n/2)!^3, n]
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