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C (standard compliant), 78 bytes
int f(int n,int k,int c){return n?n+c-k?k-c?f(n-1,k,0)+f(n-1,k,c+1):1<<n:1:0;}
pour la version lisible:
int f(int n,int k,int c){
if(n==0)return 0; // no more coin flip left => no possible path
if(n==(k-c))return 1; // last coin flip and 1 tail is lacking
...