Combinatorics and Sequence Numbers

6/13/2015

(A special note for my triskaidekaphiliac fans.)

A010966: C (n, 13): The number of ways to select 13 items from a group of n items.

The decimal expansion of the inverse of 999,999,986,000,000,090,999,999,636,000,001,000,999,997,
998,000,003,002,999,996,568,000,003,002,999,997,998,000,
001,000,999,999,636,000,000,090,999,999,986,000,000,001 produces the sequence of numbers shown in OEIS A010966, written in 9 digit strings.

1/999999986000000090999999636000001000999997998000
00300299999656800000300299999799800000100099999963
6000000090999999986000000001 =

0.
000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000001 000000014 000000105 000000560 000002380 000008568 000027132 000077520 000203490 000497420 001144066 002496144 005200300 010400600 020058300 037442160 067863915 119759850 206253075 347373600 573166440 …

What does this say?

C (n,13) = 0, if n = 0 through 12.  

C (13,13) = 1, the number of ways to select 13 items from a group of 13 is 1.

C (14,13) = 14, the number of ways to select 13 items from a group of 14 is 14.

C (15,13) = 105, the number of ways to select 13 items from a group of 15 is 105.

Etc.

David