[seqfan] Re: Two Sequences Related To Permutations of (1,2,...,n)

[Max Alekseyev]

On Sat, Jan 17, 2009 at 6:15 PM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

> (2)
>
> Let a(n) = the number of ways to fill the squares of an n-by-n grid such that there are exactly 2 filled squares, no more, no fewer, in each row and in each column of the grid.
>
> Is sequence {a(m)} already in the EIS?
>
> Is there a direct way to calculate each a(n)? It seems to me that it is VERY likely there is indeed a formula for calculating each a(n).
>
> (The reason I say this sequence is related to permutations of (1,2,...,n) is that if instead we wanted exactly ONE filled square in each row and in each column of an n-by-n grid, then the number of ways to do this would be n!, since each way represents a permutation of (1,2,3,...,n), obviously.)

That's A001499, which is also the column k=2 in A008300.

Max