[seqfan] A147681 Late-growing permutations

David Scambler dscambler at bmm.com
Fri Aug 10 09:41:30 CEST 2012

Hi Seqfans,

I note that Ron Hardin contributed a family of sequences A147681, A147682... of the form:

Late-growing permutations: number of permutations of K indistinguishable copies of 1..n with every partial sum <= the same partial sum averaged over all permutations.

I observe that in each case a(2) = Catalan(K).

Is this a recognized manifestation of the catalan numbers? I suppose that with just two species {1,2} the partial sum criterion is equivalent to down steps in Dyck paths never exceeding up steps and balancing at the end.

Also, a(3) seems to be A007004(K). Is anything known about a(4) and beyond?



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