View source for Stirling numbers of the second kind

=={{header|Prolog}}==
{{works with|SWI Prolog}}
<syntaxhighlight lang="prolog">:- dynamic stirling2_cache/3.

stirling2(N, N, 1):-!.
stirling2(_, 0, 0):-!.
stirling2(N, K, 0):-
	K > N,
	!.
stirling2(N, K, L):-
	stirling2_cache(N, K, L),
	!.
stirling2(N, K, L):-
	N1 is N - 1,
	K1 is K - 1,
	stirling2(N1, K, L1),
	stirling2(N1, K1, L2),
	!,
	L is K * L1 + L2,
	assertz(stirling2_cache(N, K, L)).

print_stirling_numbers(N):-
	between(1, N, K),
	stirling2(N, K, L),
	writef('%8r', [L]),
	fail.
print_stirling_numbers(_):-
	nl.

print_stirling_numbers_up_to(M):-
	between(1, M, N),
	print_stirling_numbers(N),
	fail.
print_stirling_numbers_up_to(_).

max_stirling2(N, Max):-
    aggregate_all(max(L), (between(1, N, K), stirling2(N, K, L)), Max).

main:-
	writeln('Stirling numbers of the second kind up to S2(12,12):'),
	print_stirling_numbers_up_to(12),
	writeln('Maximum value of S2(n,k) where n = 100:'),
	max_stirling2(100, M),
	writeln(M).</syntaxhighlight>

{{out}}
<pre>
Stirling numbers of the second kind up to S2(12,12):
       1
       1       1
       1       3       1
       1       7       6       1
       1      15      25      10       1
       1      31      90      65      15       1
       1      63     301     350     140      21       1
       1     127     966    1701    1050     266      28       1
       1     255    3025    7770    6951    2646     462      36       1
       1     511    9330   34105   42525   22827    5880     750      45       1
       1    1023   28501  145750  246730  179487   63987   11880    1155      55       1
       1    2047   86526  611501 1379400 1323652  627396  159027   22275    1705      66       1
Maximum value of S2(n,k) where n = 100:
7769730053598745155212806612787584787397878128370115840974992570102386086289805848025074822404843545178960761551674
</pre>