An oddity requiring an explanation...

[Ralf Stephan]

> Let C_n(v) denote the polynomial that counts the spanning connected  
> subgraphs of K_n according to the number of edges...
> 
> For example, C_4(v) = 16 v^3 + 15 v^4 + 6 v^5 + v^6  because K_4 has 16  
> spanning trees, 16 spanning subgraphs with 4 edges, 6 spanning  
> subgraphs with 5 edges and 1 spanning subgraph with 6 edges.
> 
> Now consider the sequence
> 
> 	C_3(-2), C_4(-2), C_5(-2), C_6(-2), C_7(-2) ...
> 
> which is
> 
> 	4, -16, 80, -512, 3904, ....
> 
> If we ignore the signs we discover that this sequence is actually the  
> series of coefficients of the expansion of (1+tan(x))/(1-tan(x)) =  
> tan(x+Pi/4) when we view this as an exponential generating function...

And if you substitute 1 instead of -2 you get A001187, and if the OEIS
were perfect there would be a line

%Y A001187 Cf. Row sums of triangle A062734.

(thanks in advance for adding this) 

%F A062734 E.g.f.: 1+ln(Sum((1+y)^binomial(n,2)*x^n/n!,n=0..infinity)).
But how to go from the e.g.f. of A062734 to tan?


ralf