Python console for SymPy 0.7.6 (Python 2.7.5)
These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)
>>> from sympy import Function, rsolve
>>> f = (n - 1)*y(n + 2) - (n**2 + 3*n - 2)*y(n + 1) + 2*n*(n + 1)*y(n)
>>> rsolve(f, y(n))
>>> from sympy import Function, rsolve
>>> from sympy.abc import n
>>> from sympy.abc import n
>>> y = Function('y')
>>> y = Function('y')
>>> f = (n - 1)*y(n + 2) - (n**2 + 3*n - 2)*y(n + 1) + 2*n*(n + 1)*y(n)
>>> rsolve(f, y(n))
>>> f = (n - 1)*y(n + 2) - (n**2 + 3*n - k)*y(n + 1) + 2*n*(n + 1)*y(n)
>>> rsolve(f, y(n))