Fix stirlings2 bug

[o314]

stirlings2 is implemented twice in this package.

• stirlings2 is correct but recursive and slow.
• nfixedsetpartitions is bugged eg. it silently overflows.

stirlings2 is slow :

julia> @btime stirlings2_new(25,7)
  17.546 μs (431 allocations: 7.09 KiB)
227832482998716310

julia> @btime stirlings2(25,7)
  594.258 μs (0 allocations: 0 bytes)
227832482998716310

nfixedsetpartitions is bugged :

@test_broken nfixedsetpartitions(21, 13) >= 0
@test_broken nfixedsetpartitions(21, 14) >= 0
@test_broken nfixedsetpartitions(21, 15) >= 0
@test_broken nfixedsetpartitions(21, 16) >= 0
@test_broken nfixedsetpartitions(21, 17) >= 0
@test_throws OverflowError nfixedsetpartitions(21,21)

SEE

• https://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
• https://dlmf.nist.gov/26.8

[codecov-io]

Codecov Report

Merging #92 into master will decrease coverage by 0.49%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master      #92      +/-   ##
==========================================
- Coverage   95.79%   95.29%   -0.50%     
==========================================
  Files           8        8              
  Lines         642      638       -4     
==========================================
- Hits          615      608       -7     
- Misses         27       30       +3     

Impacted Files	Coverage Δ
src/numbers.jl	100.00% <100.00%> (ø)
src/partitions.jl	97.10% <100.00%> (-1.00%)	⬇️
src/combinations.jl	84.03% <0.00%> (-0.72%)	⬇️

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[mschauer]

Can you use standard formatting?

[mschauer]

There is also #126, let's compare those two.