Tagged Questions
1
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2answers
70 views
Does this sequence have this interesting property relating to the prime factorization of the index?
Define a sequence as $a_0 = 0$ and $a_n$ equals the number of divisors of $n$ (including 1 and $n$) that are greater than $a_{n-1}$. This is sequence A152188 in OEIS, by the way.
(For example, the ...
0
votes
2answers
101 views
Help with $1 + a + a(a-1) + a(a-1) (a-2) +\cdots+a(a-1)\cdots(a-(n-1))$
I want to rewrite the series $$1 + a + a(a-1) + a(a-1) (a-2) +\cdots+a(a-1)\cdots(a-(n-1))$$ as $(a^n-1)Y$ or $(a^{n-1}-1)Y$
Short-form:
$$\{1+\sum_{i=1}^{n} \prod_{j=0}^{i-1}(a-j)\}$$
as $(a^n-1)Y$ ...
1
vote
1answer
107 views
Interpolation of a sequence of polynomials (viewed in terms of q-analogue powers)
I'm trying to find closed-form expressions for a sequence of coefficients, such that the index of the coefficient occurs as number such that I can later interpolate to fractional indexes as well. ...
