Stirling numbers of the second kind: Difference between revisions

do j=0 for lim+1

@.j.j = 1; if j==0 then iterate /*define the right descending diagonal.*/

@.0.j = 0; @.j.0 = 0 /* " " zero values. */

end /*j*/

do n=0 for lim+1; np= n + 1

do k=1 for lim; km= k - 1

@.np.k = k * @.n.k + @.n.km /*calculate a number in the grid. */

max#.k= max(max#.k, @.n.k) /*find the maximum value for a column. */

max#.b= max(max#.b, @.n.k) /*find the maximum value for all rows. */

end /*k*/

end /*n*/

wiwgi= max(35, length(lim+1) ) /*the maximum width of the grid's index*/

say 'row═row═' center('"columns'", max(9, max#.a + lim), '═') /*display header of the grid.*/

do r=0 for lim+1; $= $= /* [↓] display the grid to the term. */

do c=0 for lim+1 until c>=r /*build a row of grid, 1 col at a time.*/

$= $ right(@.r.c, length(max#.c) ) /*append a column to a row of the grid.*/

end /*c*/

say rightcenter(r,wi wgi) strip( substr($,2), 'T') /*display a single row of the grid. */

end /*r*/ /*stick a fork in it, we're all done. */</lang>

row═row═ ══════════════════════════════columns══════════════════════════════

0 1

1 0 1

2 0 1 1

3 0 1 3 1

4 0 1 7 6 1

5 0 1 15 25 10 1

6 0 1 31 90 65 15 1

7 0 1 63 301 350 140 21 1

8 0 1 127 966 1701 1050 266 28 1

9 0 1 255 3025 7770 6951 2646 462 36 1

10 0 1 511 9330 34105 42525 22827 5880 750 45 1

11 0 1 1023 28501 145750 246730 179487 63987 11880 1155 55 1

12 0 1 2047 86526 611501 1379400 1323652 627396 159027 22275 1705 66 1