[seqfan] Re: A147681 Late-growing permutations

[Heinz, Alois]

Am 10.08.2012 09:41, schrieb David Scambler:
> 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?

a(4) is not in OEIS:

1, 7, 403, 40350, 5223915, 783353872, 129141898872, 22745605840236,
4206489449301315, 807660192541534200, 159752979289765273698,
32371149339259024610992, 6692030708288364864188400,
1406943391115083641966787200, 300084647544974128326709244080,
64804916367088484487100154177496, 14147534294176318279439513521917987,
3118154713099658349261989389351453752,
693090538757877947419844421229560759330,
155225932761938574730157553835938696696000,
35001539803742185909212720763104652356176850

Alois