Generate sequence using previous terms sympy

Question

I would like to generate a sequence such that the previously generated element was included in the next element, I am unsure how to do this.

i.e generate the list such that its items were:

where x is just a Sympy symbol

[x,(x)*(x+1),(x)*(x+1)*(x+2)]

rather than [x,x+1,x+2]

I'm thinking something like

k.append(k*(K+o))

but I keep getting a type error

Any help greatly appreciated!

Answer 1

Maybe using a recursive lambda function and a map ?

>>> fact = lambda x: x == 0 and 1 or x * fact(x - 1)
>>> map(fact, range(4))
[1, 1, 2, 6]

and many other ways besides. If you want to return a string define your recursive function to return a string;

def fact(i):
    if i == 0:
        return 'x'
    else:
        return fact(i - 1) + '*(x+%d)' % i

and then

>>> map(fact, range(4))
['x', 'x*(x+1)', 'x*(x+1)*(x+2)', 'x*(x+1)*(x+2)*(x+3)']

and if you're using sympy and think that using strings is an "anti-pattern"

import sympy

def fact(i):
    if i == 0:
        return sympy.Symbol('x')
    else:
        return sympy.Symbol('(x+%d)' % i) * fact(i - 1)

produces

>>> map(fact, range(4))
[x, (x+1)*x, (x+1)*(x+2)*x, (x+1)*(x+2)*(x+3)*x]