Thanks very much, I appreciate your kindness.
R.E. Boss > -----Oorspronkelijk bericht----- > Van: [EMAIL PROTECTED] [mailto:programming- > [EMAIL PROTECTED] Namens bill lam > Verzonden: dinsdag 18 december 2007 4:13 > Aan: Programming forum > Onderwerp: Re: [Jprogramming] Bell numbers > > This article is not available online. > http://www.vector.org.uk/archive/v171/ > > The following is part of listing from my vector hard copy. > NB. ============================== > s2nr from Iverson's Concrete Math Companion to generate subset numbers. > s2nr=: |:@(^/~ %. ^!._1/~)@i."0 > ]a=. s2nr 10x > 1 0 0 0 0 0 0 0 0 0 > 0 1 0 0 0 0 0 0 0 0 > 0 1 1 0 0 0 0 0 0 0 > 0 1 3 1 0 0 0 0 0 0 > 0 1 7 6 1 0 0 0 0 0 > 0 1 15 25 10 1 0 0 0 0 > 0 1 31 90 65 15 1 0 0 0 > 0 1 63 301 350 140 21 1 0 0 > 0 1 127 966 1701 1050 266 28 1 0 > 0 1 255 3025 7770 6951 2646 462 36 1 > ]b=. |: 1 1 }.a > 1 1 1 1 1 1 1 1 1 > 0 1 3 7 15 31 63 127 255 > 0 0 1 6 25 90 301 966 3025 > 0 0 0 1 10 65 350 1701 7770 > 0 0 0 0 1 15 140 1050 6951 > 0 0 0 0 0 1 21 266 2646 > 0 0 0 0 0 0 1 28 462 > 0 0 0 0 0 0 0 1 36 > 0 0 0 0 0 0 0 0 1 > ]c=. b * ! i. #b > 1 1 1 1 1 1 1 1 1 > 0 1 3 7 15 31 63 127 255 > 0 0 2 12 50 180 602 1932 6050 > 0 0 0 6 60 390 2100 10206 46620 > 0 0 0 0 24 360 3360 25200 166824 > 0 0 0 0 0 120 2520 31920 317520 > 0 0 0 0 0 0 720 20160 332640 > 0 0 0 0 0 0 0 5040 181440 > 0 0 0 0 0 0 0 0 40320 > ]d=. +/ \. c > 1 2 6 26 150 1082 9366 94586 1091670 > 0 1 5 25 149 1081 9365 94585 1091669 > 0 0 2 18 134 1050 9302 94458 1091414 > 0 0 0 6 84 870 8700 92526 1085364 > 0 0 0 0 24 480 6600 82320 1038744 > 0 0 0 0 0 120 3240 57120 871920 > 0 0 0 0 0 0 720 25200 554400 > 0 0 0 0 0 0 0 5040 221760 > 0 0 0 0 0 0 0 0 40320 > > NB. ============================== > > In particular, row (column?) sum of a is bell numbers > +/"1 a > 1 1 2 5 15 52 203 877 4140 21147 > > R.E. Boss wrote: > > Where are these articles available? > > The first is not in http://www.jsoftware.com/jwiki/Articles > > > > > > R.E. Boss > > > > > >> -----Oorspronkelijk bericht----- > >> Van: [EMAIL PROTECTED] [mailto:programming- > >> [EMAIL PROTECTED] Namens bill lam > >> Verzonden: maandag 17 december 2007 15:41 > >> Aan: Programming forum > >> Onderwerp: Re: [Jprogramming] Bell numbers > >> > >> FYI, Eugene McDonnell contributed an article in Vector > >> McDonnell, Eugene, At Play with J: Blists in OLEIS, Vol 17.1, 110 > >> and a technical correspondence in Vol 17.2, 112 > >> It shows Bell number is the row sum of Stirling subset numbers. > >> > >> Joseph De Kerf discussed calculation of Bell number using floating > point > >> in APL, > >> De Kerf, Joseph, Bell Numbers and APL, Vol 17.1, 131 > >> > >> -- > >> regards, > >> bill > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > -- > regards, > bill > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
