#include <stdio.h>

int pa2re1(int i, int j, int n);
int po(int i, int j);
int pa2re2(int i, int j, int n);
int bi(int i, int j);
int pa(int i, int j, int n);

main()
{
  int m=11;

  int vpa;
  int vpa2re2;
  int bipa;
  int bipa2re2;

  for(int n=m-2;n<=2*(m-1)+m-2;n++)
  {
    vpa=pa(1,m,n);
    vpa2re2=pa2re2(1,m,n);

    bipa=bi((m-1)*2+m-2,n);
    bipa2re2=bi((m-1)*2,n);

    printf("%2d %12d %12d %10f %12d %12d %10f\n",n,
      vpa,bipa,(double)vpa/bipa,
      vpa2re2,bipa2re2,(double)vpa2re2/bipa2re2);
  }
}

int pa(int i, int j, int n)
{
  if(!(n>=0 && j>i && i>=1)) return 0;

  if(n<j-i-1 || n>2*(j-i)+j-i-1) return 0;

  int v=0;

  v+=pa2re2(i,j,n);

  for(int k=i+1;k<=j-1;k++)
  {
    for(int nn=k-i-1;nn<=n-1-(j-k-1);nn++)
      v += pa2re2(i,k,nn) * pa(k,j,n-1-nn);
  }

  return v;
}

int pa2re2(int i, int j, int n)
{
  if(!(n>=0 && j>i && i>=1)) return 0;

  if(n<j-i-1 || n>2*(j-i)) return 0;

  if(j-i==1)
  {
    if(n==0) return 1;
    else if(n==1) return 2;
    else if(n==2) return 1;
    else 0;
  }

  int v=0;

  v+=pa2re1(i,j,n);

  v+=pa2re2(i+1,j,n-2);

  v+=pa2re1(i,j-1,n-2);

  for(int k=i+1;k<=j-2;k++)
  { 
    v+=pa2re1(i,k,k-i) * pa2re2(k+1,j,n-2-(k-i));
    v+=pa2re1(i,k,k-i-1) * pa2re2(k+1,j,n-2-(k-i-1));
  }

  return v;
}


int pa2re1(int i, int j, int n)
{
  //two original packets at positions i and j and n redundant packets
  //but no more than one redundant packet for each pair
  if(!(n>=0 && j>i && i>=1)) return 0;
  if(n==j-i) return 1*po(2,j-i);
  else if(n==j-i-1) return (j-i)*po(2,j-i-1);
  else return 0;
}

int po(int i, int j)
{
  int v = 1;
  for(int jj=1;jj<=j;jj++)
    v*=i;
  return v;
}

int bi(int i, int j)
{
  if(!(i>=j && j>=0)) return 0;
  if(i==0) return 1;
  if(j==0) return 1;
  return bi(i,j-1)*(i-j+1)/j;
}