Bell numbers: Difference between revisions

=={{header|ALGOL-M}}==

<lang algolm>begin

integer function index(row, col);

integer row, col;

index := row * (row-1)/ 2 + col;

integer ROWS; ROWS := 15;

begin

decimal(11) array bell[0:ROWS*(ROWS+1)/2];

integer i, j;

bell[index(1, 0)] := 1.;

for i := 2 step 1 until ROWS do

begin

bell[index(i, 0)] := bell[index(i-1, i-2)];

for j := 1 step 1 until i-1 do

bell[index(i,j)] := bell[index(i,j-1)] + bell[index(i-1,j-1)];

end;

write("First fifteen Bell numbers:");

for i := 1 step 1 until ROWS do

begin

write(i);

writeon(": ");

writeon(bell[index(i,0)]);

end;

write("");

write("First ten rows of Bell's triangle:");

for i := 1 step 1 until 10 do

begin

write("");

for j := 0 step 1 until i-1 do

writeon(bell[index(i,j)]);

end;

end;

end</lang>

{{out}}

<pre>First fifteen Bell numbers:

1: 1.0

2: 1.0

3: 2.0

4: 5.0

5: 15.0

6: 52.0

7: 203.0

8: 877.0

9: 4140.0

10: 21147.0

11: 115975.0

12: 678570.0

13: 4213597.0

14: 27644437.0

15: 190899322.0

First ten rows of Bell's triangle:

1.0

1.0 2.0

2.0 3.0 5.0

5.0 7.0 10.0 15.0

15.0 20.0 27.0 37.0 52.0

52.0 67.0 87.0 114.0 151.0 203.0

203.0 255.0 322.0 409.0 523.0 674.0 877.0

877.0 1080.0 1335.0 1657.0 2066.0 2589.0 3263.0 4140.0

4140.0 5017.0 6097.0 7432.0 9089.0 11155.0 13744.0 17007.0 21147.0

21147.0 25287.0 30304.0 36401.0 43833.0 52922.0 64077.0 77821.0 94828.0 115975.0</pre>