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revised 
Important formulas in Combinatorics
Elaborated on tree reps 
Aug
27 
revised 
Important formulas in Combinatorics
Introduced missing signs 
Aug
27 
revised 
Important formulas in Combinatorics
deleted 6 characters in body 
Aug
27 
answered  Important formulas in Combinatorics 
Aug
27 
revised 
Important formulas in Combinatorics
noted differences from Duchamp's answer 
Aug
26 
comment 
Important formulas in Combinatorics
@Duchamp, for Pourchet note see books.google.com/… 
Aug
26 
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Important formulas in Combinatorics
On a historical note: Comtet mentions Prouhet or Pourchet on page 220 of his book Adv. Comb. (Reidel, 1974) in relation to the Faa di Bruno formula. I couldn't track that down. Do you know of his contribution? 
Aug
26 
comment 
Important formulas in Combinatorics
Cf. also arxiv.org/abs/0910.0695 and the related arxiv.org/abs/1205.2097 on cumulants. 
Aug
26 
comment 
Important formulas in Combinatorics
@Duchamps, I made the connection to binomial Sheffer sequences explicit and referenced a CayleyComtet tree rep. 
Aug
26 
revised 
Important formulas in Combinatorics
Elucidated relation to umbral calculs / binomial Sheffer sequences 
Aug
25 
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Important formulas in Combinatorics
@Duchamp, thanks, I had actually missed that particular ref, but have been aware of your group's numerous, excellent contributions with the emphasis on relations to quantum physics. 
Aug
25 
revised 
Important formulas in Combinatorics
Added historical notes 
Aug
25 
revised 
Pochhammer symbol of a differential, and hypergeometric polynomials
historical note on Poole 
Aug
25 
revised 
Important formulas in Combinatorics
Added connections to other combinatoric structures. 
Aug
21 
revised 
Important formulas in Combinatorics
Noted relation to Eulerian numbers. Deleted some extraneous statements. 
Aug
20 
answered  Important formulas in Combinatorics 
Aug
19 
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Hopf Algebra for a physicist
For more intros to Hopf algebras in physics, see arXiv papers jointly authored by Blasiak, Duchamp, Horzela, Penson and Solomon, and papers by Figueroa and GraciaBondi. 
Aug
11 
answered  Generalizing a problem to make it easier 
Aug
7 
comment 
What does Mellin inversion “really mean”?
See also tcjpn.wordpress.com/2015/08/05/… 
Aug
4 
comment 
Derivative in terms of finite differences
math.stackexchange.com/questions/892961/… 