Signals

This is from a poster RAL and CDL gave me, and that is an enlarged photocopy from an unknown book.

2 people	2 signals
3 people	9 signals
4 people	28 signals
5 people	75 signals
6 people	186 signals
7 people	441 signals
8 people	1,016 signals
9 people	2,295 signals
10 people	5,110 signals
11 people	11,253 signals
12 people	24,564 signals
13 people	53,235 signals
14 people	114,674 signals
15 people	245,745 signals
16 people	524,272 signals
17 people	1,114,095 signals
18 people	2,359,278 signals
19 people	4,980,717 signals
20 people	10,485,740 signals
21 people	22,020,075 signals

A mathematically inclined friend thought the equation that explained the relationship between the People and Signals was

S=(p*((2^(p-1))-1)