/*
 * Calculate I_n = \int_0^1 e^{x-1} x^n dx
 *
 * integrating by parts, I_n = 1 - n*I_{n-1}
 */

#include <stdio.h>
#include <math.h>

#define J 30

int main(void) {
    double i[J+1], p[J+1];
    int j;

    i[0] = 1 - 1/exp(1.);  /* I_0 */

    for (j = 1; j <= J; j++) {
        i[j] = 1. - j*i[j-1];   /* I_n = 1 - n*I_{n-1} */
    }
    
    p[J] = 10.; 
    for (j = J; j >= 0; j--) {
        p[j] = (1. - p[j+1])/(j+1);   /* I_n = (1 - I_{n+1})/(n+1) */
    }
    
    for (j = 0; j <= J; j++) {
        printf("%3d    %25.6f   %25.6f\n", j, i[j], p[j]);
    }

    return(0);
}