The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4)+O(1), its Variance is (n/log(4))(1/log(4)-1/2) and It is Asymptotically Normal! (An Experimental-Mathematical Proof)

The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4)+O(1), its Variance is (n/log(4))(1/log(4)-1/2)+O(1) and It is Asymptotically Normal! (An Experimental-Mathematical Proof)
By Shalosh B. Ekhad
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Written: June 28, 2011.
This article was inspired by my master's quickie that was inspired, in turn by Dan Haran's Email message . I was wondering what happens when you replace -1 by t, and asked about the statistical properties of the distribution "number of blocks" in the poplulation of ordered set partitions.
The conclusions of this article were obtained by running the input file with the Maple program OSP (kindly written by Doron Zeilberger), that generated the output file .
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
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