Ondrej Sika

Kombinacni cisla

${0 \choose 0} = 1$
${1 \choose 0} = 1$	${1 \choose 1} = 1$
${2 \choose 0} = 1$	${2 \choose 1} = 2$	${2 \choose 2} = 1$
${3 \choose 0} = 1$	${3 \choose 1} = 3$	${3 \choose 2} = 3$	${3 \choose 3} = 1$
${4 \choose 0} = 1$	${4 \choose 1} = 4$	${4 \choose 2} = 6$	${4 \choose 3} = 4$	${4 \choose 4} = 1$
${5 \choose 0} = 1$	${5 \choose 1} = 5$	${5 \choose 2} = 10$	${5 \choose 3} = 10$	${5 \choose 4} = 5$	${5 \choose 5} = 1$
${6 \choose 0} = 1$	${6 \choose 1} = 6$	${6 \choose 2} = 15$	${6 \choose 3} = 20$	${6 \choose 4} = 15$	${6 \choose 5} = 6$	${6 \choose 6} = 1$
${7 \choose 0} = 1$	${7 \choose 1} = 7$	${7 \choose 2} = 21$	${7 \choose 3} = 35$	${7 \choose 4} = 35$	${7 \choose 5} = 21$	${7 \choose 6} = 7$	${7 \choose 7} = 1$
${8 \choose 0} = 1$	${8 \choose 1} = 8$	${8 \choose 2} = 28$	${8 \choose 3} = 56$	${8 \choose 4} = 70$	${8 \choose 5} = 56$	${8 \choose 6} = 28$	${8 \choose 7} = 8$	${8 \choose 8} = 1$
${9 \choose 0} = 1$	${9 \choose 1} = 9$	${9 \choose 2} = 36$	${9 \choose 3} = 84$	${9 \choose 4} = 126$	${9 \choose 5} = 126$	${9 \choose 6} = 84$	${9 \choose 7} = 36$	${9 \choose 8} = 9$	${9 \choose 9} = 1$
${10 \choose 0} = 1$	${10 \choose 1} = 10$	${10 \choose 2} = 45$	${10 \choose 3} = 120$	${10 \choose 4} = 210$	${10 \choose 5} = 252$	${10 \choose 6} = 210$	${10 \choose 7} = 120$	${10 \choose 8} = 45$	${10 \choose 9} = 10$	${10 \choose 10} = 1$

Python generator

import itertools

def comb(n, k):
    return len(list(itertools.combinations(range(n), k)))

res = []
for n in xrange(11):
    res2 = []
    for k in xrange(11):
        if n >= k:
            res2.append((n, k, comb(n, k)))
        else:
            res2.append(None)
    res.append(res2)

print '<table>',
for row in res:
    print '<tr><td>',
    print '</td><td>'.join(map(lambda x: '${%s \\choose %s} = %s$'% x if x else '', row)),
    print '</td></tr>',
print '</table>'