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Karl, it's very nice to have this article. But the changes you made to the linked articles seemed very wrong to me for some reason:
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Participate in the deletion discussions at the nomination pages linked above. —
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Anton, I agree with your changes. Further thought, suggests that
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467:{\displaystyle C_{k,n+p}-C_{k,n}={\frac {kp}{2}}(2n+p-1)}
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