# formule des Chudnovsy pour pi
A := 13591409;
B := 545140134;
C := 640320^3;
rec := { (A+B*n) * (3*n+3)* (3*n+2)*(3*n+1) * (n+1)^3 * C * u(n+1)
         + (6*n+6)*(6*n+5)*(6*n+4)*(6*n+3)*(6*n+2)*(6*n+1) * (A+B*(n+1)) * u(n),
         u(0) = A };
bound_rec(rec, u(n));

# permutations de Baxter
rec := { (n+2)*(n+3)*a(n) = (7*n^2+7*n-2)*a(n-1) + 8*(n-1)*(n-2)*a(n-2), a(0)=1, a(1)=1 };
bound_rec(rec, a(n));

# involutions, cf. Wimp & Zeilberger1985, ex. 2.1
rec := { (n+1)*t(n) + t(n+1) - t(n+2), t(0) = 1, t(1) = 1 };
bound_rec(rec, t(n));

# une intégrale, cf. Wimp & Zeilberger1985, ex. 2.3
rec := { 2*i(n+3) = (n+2)*i(n+1)+i(n), i(0)=1/5, i(1)=1/5, i(2)=1/5 };
bound_rec(rec, i(n));
