requesting scan of p. 228 from Symmetric Function and Allied Tables (1966)

[Natalia L. Skirrow]

I have been working on a page about the third kind of Stirling number, and A008969 (a number triangle that scales by powers of factorials to make entries integer) lists SFaAT as describing them on p. 228; other sections have been uploaded to the OEIS, and an inter-library loan will likely be expensive, can anyone who has the book scan and upload the relevant excerpt?

[Neil Sloane]

Here you go!  Can you upload it yourself to the sequence?

Best regards

Neil 

Neil J. A. Sloane, Chairman, OEIS Foundation.

Also Visiting Scientist, Math. Dept., Rutgers University, 

Email: njas...@gmail.com

On Tue, Oct 14, 2025 at 9:14 AM Natalia L. Skirrow <dronebetter...@gmail.com> wrote:

I have been working on a page about the third kind of Stirling number, and A008969 (a number triangle that scales by powers of factorials to make entries integer) lists SFaAT as describing them on p. 228; other sections have been uploaded to the OEIS, and an inter-library loan will likely be expensive, can anyone who has the book scan and upload the relevant excerpt?

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[Brendan]

Here is Maple code, which should be easy to translate to other languages.

S := proc(n,r,j) option remember;
        if n = 0 then 1/j^r;
        else S(n-1,r,j+1)-S(n-1,r,j)
        end if;
end proc;
A := (n,r) -> ((n+1)!)^r * abs(S(n,r,1)) / n!;

Eg,

> A(10,12)
4498607227742743734699578157092398416324947564107251882145271134895996928000000000000

Brendan.

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[Jon Wild]

Dear list,

There was some discussion around sequence A250001 a few weeks ago, and
at some point someone asked about extending the problem to arrangements
of circles where more than 2 circles are allowed to pass through the
same point. This isn't yet that full problem, but I was thinking about
how many ways that intersection point could look like, locally, when
there are n circular arcs passing through it (disregarding intersections
elsewhere in the arrangement if the arcs were extended to full circles).
It turned out to be not very hard to calculate, as it's equivalent to a
word combinatorics problem, a simple enough one that I even wonder if
there's a closed-ish form for a(n).

Anyway the resulting sequence is now A387988, and there are some quite
pretty pictures to look at, like https://oeis.org/A387988/a387988_2.svg
which shows the 33 solutions for n=5. (There are simple black-and-white
illustrations too, for those who prefer them.) The sequence has been
reduced for mirror symmetry but I should be able to create the one-sided
version soon.

Jon Wild