21–30 of 46 posts
Earlier quoted context omitted.
As I understand it, written in Go. There's a mildly humorous "How do you know" exchange where someone on HN quizzes the very person most likely to know: https://news.ycombinator.com/item?id=9920020
HN has had a couple of those.
The OEIS lives here: https://oeis.org/ Super useful resource.
OEIS foundation: http://oeisf.org/ It's nice to see they have a solid plans on how to keep the website running indefinitely.
>"My fascination with these sequences began in 1964 when I was a graduate student at Cornell University in Ithaca, NY, studying neural networks. I had encountered a sequence of numbers, 1, 8, 78, 944, 13800, . . ., and I badly needed a formula for the n-th term, in order to determine the rate of growth of the terms..." Related Mathologer video: Mathologer - "Why don't they teach Newton's calculus of 'What comes next?…
The finite difference method of that video is only useful for finding polynomial sequences. Of course, any finite sequence can be extended to some polynomial, but in many cases (such as this one) that’s not the result you’re looking for.
Earlier quoted context omitted.
The finite difference method of that video is only useful for finding polynomial sequences. Of course, any finite sequence can be extended to some polynomial, but in many cases (such as this one) that’s not the result you’re looking for.
Specifically, in this case, why isn't it?
a(n) = (n-1)! * Sum_{k=0..n-2} n^k/k!
a(n) ~ sqrt(Pi/2)*n^(n-1/2)
from math import factorial
from fractions import Fraction as F
def A000435(n):
return int(factorial(n-1) *
sum(F(n**k, factorial(k)) for k in range(0, n-1)))
def A000127(n):
return (n**4 - 6*n**3 + 23*n**2 - 18*n + 24)//24>"My fascination with these sequences began in 1964 when I was a graduate student at Cornell University in Ithaca, NY, studying neural networks. I had encountered a sequence of numbers, 1, 8, 78, 944, 13800, . . ., and I badly needed a formula for the n-th term, in order to determine the rate of growth of the terms..." Related Mathologer video: Mathologer - "Why don't they teach Newton's calculus of 'What comes next?…
The finite difference method of that video is only useful for finding polynomial sequences. Of course, any finite sequence can be extended to some polynomial, but in many cases (such as this one) that’s not the result you’re looking for.
> Robert Jackson suggests that if you've completed a difference table and still don't understand the sequence, you should turn the paper through an angle of 60 degrees, say, and start again and perhaps repeat this several times to make a fan of difference tables.