Stirling numbers of the first kind: Difference between revisions
Added Algol W
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Maximum Stirling number of the first kind with n = 100:
19710908747055261109287881673376044669240511161402863823515728791076863288440277983854056472903481625299174865860036734731122707870406148096000000000000000000
</pre>
=={{header|ALGOL W}}==
<lang algolw>begin % show some (unsigned) Stirling numbers of the first kind %
integer MAX_STIRLING;
MAX_STIRLING := 12;
begin
% construct a matrix of Stirling numbers up to max n, max n %
integer array s1 ( 0 :: MAX_STIRLING, 0 :: MAX_STIRLING );
for n := 0 until MAX_STIRLING do begin
for k := 0 until MAX_STIRLING do s1( n, k ) := 0
end for_n ;
s1( 0, 0 ) := 1;
for n := 1 until MAX_STIRLING do s1( n, 0 ) := 0;
for n := 1 until MAX_STIRLING do begin
for k := 1 until n do begin
integer s1Term;
s1Term := ( ( n - 1 ) * s1( n - 1, k ) );
s1( n, k ) := s1( n - 1, k - 1 ) + s1Term
end for_k
end for_n ;
% print the Stirling numbers up to n, k = 12 %
write( "Unsigned Stirling numbers of the first kind:" );
write( " k" );
for k := 0 until MAX_STIRLING do writeon( i_w := 10, s_w := 0, k );
write( " n" );
for n := 0 until MAX_STIRLING do begin
write( i_w := 2, s_w := 0, n );
for k := 0 until n do begin
writeon( i_w := 10, s_w := 0, s1( n, k ) )
end for_k
end for_n
end
end.</lang>
{{out}}
<pre>
Unsigned Stirling numbers of the first kind:
k 0 1 2 3 4 5 6 7 8 9 10 11 12
n
0 1
1 0 1
2 0 1 1
3 0 2 3 1
4 0 6 11 6 1
5 0 24 50 35 10 1
6 0 120 274 225 85 15 1
7 0 720 1764 1624 735 175 21 1
8 0 5040 13068 13132 6769 1960 322 28 1
9 0 40320 109584 118124 67284 22449 4536 546 36 1
10 0 362880 1026576 1172700 723680 269325 63273 9450 870 45 1
11 0 3628800 10628640 12753576 8409500 3416930 902055 157773 18150 1320 55 1
12 0 39916800 120543840 150917976 105258076 45995730 13339535 2637558 357423 32670 1925 66 1
</pre>
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