How to create a vector with a sequence 1, u, u(u-1), u(u-1)(u-2)....

How to create a vector with a sequence 1, u, u(u-1), u(u-1)(u-2)....

[Rik]

What have you tried so far, and what do you mean by u, can you give an example?

[Walter Roberson]

What is the mathematics behind 1 being present at the beginning of the sequence? The rest is easy to state mathematically in terms of the pochhammer symbol, but the 1 does not appear to fit.

[PJS KUMAR]

Ok. Give the code for rest of the sequence. I will try to fit 1 into the victor.

[PJS KUMAR]

I tried as

A(1)=1;
For i=2:n
A(i)=A(i-1)*(u-(i-2))

[Walter Roberson]

Does u(u-1) indicate indexing u at index u-1 or does it indicate multiplying the scalar u by (the scalar u minus 1)?

Answer 1

[Walter Roberson]

syms u
n = 7;
A = [1,cumprod(u - (0:n))];

A =
[ 1, u, u*(u - 1), u*(u - 1)*(u - 2), u*(u - 1)*(u - 2)*(u - 3), u*(u - 1)*(u - 2)*(u - 3)*(u - 4), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5)*(u - 6), u*(u - 1)*(u - 2)*(u - 3)*(u - 4)*(u - 5)*(u - 6)*(u - 7)]

Answer 2

[KALYAN ACHARJYA]

u=input('Enter the value of u (more than 1): ');
n=input('Enter the numbers of Elements required: ');
a(1)=1;
for i=2:n
      a(i)=a(i-1)*(u-i+2);
end
disp(a);

[PJS KUMAR]

Thank you for your response. But I want the vector in terms of 'u' only, without taking value for 'u'.

[Rik]

At some point you'll have to enter a value for u. Or do you plan on using the symbolic toolbox for further analysis?