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binomio de newton em C


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Estou fazendo um programa pra faculdade que tem que calcular  uma soma dupla vezes um coef. B. Porém o valor de B é sempre zero e os da somatoria não são corretos.

#include <stdio.h>
#include <math.h>   
#include <stdlib.h>
   
double fatorial(double w){
double fat;
for(fat = 1; w > 1; w = w - 1)
fat = fat * w;
 return fat;
}

    
  int main(){
        int p, l, k, i, N;
        double B, func, n, m, somatorio1, somatorio2, soma = 0., b;;
    printf("Digite os valores de n m :\n");
    scanf("%lf %lf", &n, &m);
    N = n + m;
    for(k = 0; k <= N; k++){
    
    func =  fatorial(k) / ( pow(2, N) * fatorial(n) * fatorial(m));
        B = sqrt(func);

    for(p = 0;p <= n; p++){
        for(l = 0;l <= m; l++){ 
            if(p+l == k){
                somatorio1 = pow(-1, p) *(fatorial(n) / (fatorial(p) * fatorial(n - p)));
                somatorio2 = fatorial(m) / (fatorial(l) * fatorial(m - l)); 
                soma = soma + somatorio1 * somatorio2;
            }
    
        }
    }
printf("%d %lf\n", k, soma);
    }    
       return 0;
   }

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