A Function With Integer Derivatives

[Joshua Zucker]

A couple more rows of the triangle:
for n = 11,
{-10713432820904088, 
-617553818644875840, 
-25157461853018459328, 
-517771007699136629760, 
31015736154089675723520, 
5106735657220965504353280, 
438354730400167790676595008, 
28095533201475267740414521344, 
1299131328877082089834243155840, 
13375644946554171365035134382080, 
-7516739529239038990381442809422720}

and for n = 12,
{-1391515001750734848, 
-64700944064601044928, 
-1715316294903802416000, 
60116116886510831665920, 
13675594534359812245585920, 
1324651669744456425705473088, 
94478303926547635606895241216, 
4908750920629043479202263835520, 
91860376434740784967094609264640, 
-20178146401867794744065247411450240, 
-3441942595981979445452283970462310400, 
-509642295441857110859207666163306627456}

and for n = 13,
{-153916832046717055680, 
-5002390938338783619840, 
  88949369589780365233920, 
33449078289425073856650240, 
3675758997021895031355920448, 
290137860633015477170610905088, 
16937645633411620936496603091840, 
457792166085396904825674294620160, 
-57827295505778751014546763528923520, 
-12869095876451895526245866003559874560, 
-1644692641302568988873297011810124163456, 
-149062464595059323650041567777045571584000, 
-13636312188249938084473031318239952020992000}
this last one taking 2 minutes of CPU time, not too bad yet...

n = 14,
{-13192031943538520929920, 
59040811110952025982720, 
75243525224284467222773760, 
9451378457141825048756897088, 
823971936017205724572634429440, 
53639803028156187660122072419200, 
1883189954886758430614446572011520, 
-146353050772134156469282662070381440, 
-41516212490664390189546301111129989120, 
-5801884547240686607327691232395490302336, 
-610098946181858392937632129545282650112000,
-49482342869053163637025145553266058607872000, 
-2048800463059287645192431843169629875791667200, 
280408673646163079829005356798869929630576140800}
in 4 minutes of CPU time, 

so in the morning I can generate more terms if anyone's interested.

By the way, superseeker doesn't say anything useful about this
sequence that I can find (i only tried the first column; I didn't try
the diagonal yet).

--Joshua Zucker
PS: I haven't checked my code -- I figure someone out there should at
least check a couple of the small cases by hand or by another computer
algorithm to make sure that the answers agree.  I wouldn't submit this
to OEIS without at least a little more checking.