Fix PARI formula generation for rising factorial when base can be zero

[Copilot]

• Investigate the issue with PARI formula for A006430
• Identify the root cause: rising factorial formula (a+b-1)!/(a-1)! generates undefined (-1)! when a=0
• Implement fix to use product expansion when the factorial denominator can be negative
• Add test for A006430 PARI formula
• Verify the fix with existing tests
• Run code review and security checks
• Add range check before Number.asInt() to avoid exception for large numbers
• Simplify logic and improve comments based on code review feedback

Summary

This PR fixes an issue with PARI/GP formula generation for sequences like A006430 where the rising factorial operation fac a,b (b > 0) would generate an invalid factorial expression when the base a could be zero.

Problem

When generating PARI/GP formulas for rising factorials, the code would generate expressions like (a+b-1)!/(a-1)!. For A006430, when n=1, the base expression evaluates to 0, making the denominator (-1)! which is undefined in PARI/GP.

Solution

The fix extends the product expansion approach (already used for small constant values of b) to handle all cases where b is within the MAX_PRODUCT_EXPANSION threshold (±10). This ensures that when a can be zero, the formula uses an explicit product like a*(a+1)*(a+2)*(a+3) instead of the factorial division form (a+3)!/(a-1)!.

Key changes

• Added range check in Number format before calling asInt() to avoid exceptions
• Simplified the logic by removing redundant conditional
• Updated comments to clarify the intent of the range check

Original prompt

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This section details on the original issue you should resolve

<issue_title>Test PARI formula for A006430</issue_title>
<issue_description>It seems there is a problem with factorial usage in PARI for A006430. Please check.</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Test PARI formula for A006430 #614

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[ckrause]

@copilot Number.asInt() throws an exception if the number is too large. Avoid this by first doing a range check in the Number format.

[Copilot]

@copilot Number.asInt() throws an exception if the number is too large. Avoid this by first doing a range check in the Number format.

Added a range check using Number comparisons (b.value >= Number(-MAX_PRODUCT_EXPANSION) && b.value <= Number(MAX_PRODUCT_EXPANSION)) before calling asInt() in commit 94f1e1a.