A304036 Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... .
1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 4, 3, 5, 2, 4, 2, 5, 3, 4, 1, 2, 1, 3, 2, 3, 1, 2
Offset: 0
Examples
a(6) = 3 because we have [6], [2,2,2] and [2,2,1,1].
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- Wikipedia, Factorial number system
Formula
G.f.: Product_{j>=1} Sum_{k=0..j+1} x^(k*j!) = Product_{j>=1} (1-x^((j+1)!+j!))/(1-x^(j!)).