[seqfan] Re: A180388-A180389 pops up in unexpected place (Re: PS: Permutation Ascents )

[wouter meeussen]

now verified upto n=12 (169974040).

so these
"Number of permutations of 1..n with number of rises (p(i+1)>p(i)) the same
as number of rises in the inverse permutation" magically equal the
"sum of squares of the coefficients of the (numerators of) the G.F. f(v) for
the count of monomials in the Schur polynomials of (all partitions of the)
degree n, in function of the number of variables v."

(quite a mouth-full, but anything Schur-ish tends to verbosity)

For me, A180389 can be the sequence of the month, but it needs more
documentation.
How was it calculated?
Ron, Leroy, D.S., could you oblige?

Wouter.

----- Original Message ----- 
From: "Meeussen Wouter (bkarnd)" <wouter.meeussen at vandemoortele.com>
To: "'Sequence Fanatics Discussion list'" <seqfan at list.seqfan.eu>
Sent: Thursday, October 28, 2010 11:55 AM
Subject: [seqfan] A180388-A180389 pops up in unexpected place (Re: PS:
Permutation Ascents )


> see http://list.seqfan.eu/pipermail/seqfan/2010-August/005856.html
>
> this pops up unexpectedly in a study of the count of monomials in the
Schur polynomials (generated by the partitions).
> I can only verifiy correspondence up to n=8:   1, 2, 6, 22, 96, 492, 2952,
20588 .. combinatoricBoom...
> and are aware of the trap of the SLSN (Strong Law of Small Numbers).
>
> Can anyone help find a closed form, or more connections between A180389
and integer partitions?
>
> Wouter.
>