8812: [CSES Problem Set] Functional Graph Distribution
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Description
A functional graph is a directed graph where each node has outdegree 1. For example, here is a functional graph that has 9 nodes and 2 components:
Given n, your task is to calculate for each k=1…n the number of functional graphs that have n nodes and k components.
Input
The only input line has an integer n: the number of nodes.
Output
Print n lines: for each k=1…n the number of graphs modulo $10^9+7$.
Constraints
$1≤n≤5000$
Sample 1 Input
3
Sample 1 Output
17
9
1