request for a b-file for a core file

[Christian G. Bower]

I just sent a b-file of terms 0-500 to Neil for A001678.
I'm still working on a version for A000014

------ Original Message ------
From: "N. J. A. Sloane" <njas at research.att.com>
To: seqfans at seqfan.net, seqfan at ext.jussieu.frCc: njas at research.att.com
Subject: request for a b-file for a core file

> 
> Could someone help produce a b-file for A000014?
> (and A001678 along the way)
> 
> Here is the sequence:
> 
> %I A000014 M0320 N0118
> %S A000014
0,1,1,0,1,1,2,2,4,5,10,14,26,42,78,132,249,445,842,1561,2988,5671,10981,
> %T A000014
21209,41472,81181,160176,316749,629933,1256070,2515169,5049816,10172638,
> %U A000014
20543579,41602425,84440886,171794492,350238175,715497037,1464407113
> %N A000014 Number of series-reduced trees with n nodes.
> 
> 
> I could use 200, or 500 or so terms
> 
> Notes on computing A14 and A1678:
> 
> looking at the H'book of Graph Theory, p. 525:
> 
> they define f(x) (essentially A1678 but with a different offset):
> f(x) = 1*x+1*x^3+1*x^4+2*x^5+3*x^6+6*x^7+10*x^8+19*x^9+35*x^10+...
> 
> by
> 
> f = (x/(x+1))* exp( sum( f(x^i) / i, i=1..infinity ) )
> 
> then A14 is given by
> 
> (1+x)f(x) - ((1+x)/2) f(x)^2 + ((1-x)/2) f(x^2)
> 
> = x + x^2 + x^4 + x^5 + 2 x^6 + ...
> 
> = A14
> 
> I actually haven't checked these formulae - there are
> slightly different versions in the entry for A14 itself.
> 
> Thanks!
> 
> Neil
> 
>