I'm puzzled by A129947

[Jonathan Post]

I'm puzzled by A129947 a(n) = k!/T(k-1), where k is a positive integer.

If T(n) means n-th triangular number = A000217(n) = n*(n+1)/2 then we have:

k!/T(k-1) = [1 * 2 * 3 * 4 * ... * (k-1) * k] / [(k-1)*k/2]
= 2 * [1 * 2 * 3 * 4 * ... *(k-1) * k] / [(k-1)*k]
= 2 * [1 * 2 * 3 * 4 * ... (k-2)] = 2*(k-2)!

We have 2*(k-2)! = 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760 (all
in A129947),

then 7257600 (not in A129947)

then 79833600, 958003200, ...

So is A129947 just 1 U 3 U 2*(n-2)! but accidently missing 2*(12-2)! I
wonder? Or am I misunderstanding the definition?

One might also look at the array A[k,n] = {n! / j-th k-gonal number for some j}.



Jonathan is right, there is definitely something wrong
with that sequence

It appears to be an erroneous version of either of these two:

%S A052849 ,0,2,4,12,48,240,1440,10080,80640,725760,7257600,79833600,958003200,12454041600,174356582400,2615348736000,41845579776000,711374856192000,12804747411456000,243290200817664000,4865804016353280000,
%S A098558 ,1,2,4,12,48,240,1440,10080,80640,725760,7257600,79833600,958003200,12454041600,174356582400,2615348736000,41845579776000,711374856192000,12804747411456000,243290200817664000,4865804016353280000,

I am going to delete it!

NJAS