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
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regards,
bill
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