Problem
The rhyme scheme for a poem (or stanza of a longer poem) tells which lines of the poem rhyme with which other
lines. For example, a limerick such as
If computers that you build are quantum
Then spies of all factions will want 'em
Our codes will all fail
And they'll read our email
¡®Til we've crypto that's quantum and daunt 'em
Jennifer and Peter Shor (http://www.research.att.com/~shor/notapoet.html)
Has a rhyme scheme of aabba, indicating that the first, second and fifth lines rhyme and the third and fourth lines
rhyme.
For a poem or stanza of four lines, there are 15 possible rhyme schemes:
aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abba, abbb, abbc, abca, a bcb, abcc, and abcd.
Write a program to compute the number of rhyme schemes for a poem or stanza of N lines where N is an input
value.
Input
Input will consist of a sequence of integers N, one per line, ending with a 0 (zero) to indicate the end of the data. N
is the number of lines in a poem.
Output
For each input integer N, your program should output the value of N, followed by a space, followed by the number
of rhyme schemes for a poem with N lines as a decimal integer with at least 12 correct significant digits (use double
precision floating point for your computations).
Example
Input
1
2
3
4
20
30
10
0
Output
1 1
2 2
3 5
4 15
20 51724158235372
30 846749014511809120000000
10 115975