Generating function for terms of Euler triangle?

Thread starter ktoz
Start date Sep 15, 2005
Tags

Euler Function Generating function Terms Triangle

AI Thread Summary

The discussion revolves around finding the generating function for the terms of the Euler triangle. After some difficulty in locating the formula, the user discovers it on the OEIS (Online Encyclopedia of Integer Sequences) website. The formula for generating the terms is provided as A(n,k)=Sum (-1)^j*(k-j)^n*C(n+1,j), where j ranges from 0 to k. The user shares this information for others who may be searching for the same formula. This highlights the importance of utilizing resources like OEIS for mathematical inquiries.

Sep 15, 2005

ktoz

I'm sure this is relatively easy, but after an hour or so googling, I can't seem to find the formula for generating terms of the http://steiner.math.nthu.edu.tw/chuan/123/test/euler.htm

Is this known by some other name? Maybe that's why I can't find it?

Thanks

Last edited by a moderator: May 2, 2017

Mathematics news on Phys.org

Sep 16, 2005

ktoz

Found it at Sloan's

For anyone else who's interested, the formula is:

A(n,k)=Sum (-1)^j*(k-j)^n*C(n+1,j), j=0..k

and the link is here here

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...

View full post »

Thread 'Fixing Things Which Can Go Wrong With Complex Numbers'

Greg tells me the feature to generate a new insight announcement is broken, so I am doing this: https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/

View full post »