Comment on A71879

[Roland Bacher]

Dear Sequence-fans,

sequence A71879 has the following cryptic comment by E Deutsch which 
I do not understand.:

	COMMENT 	

Number of ordered trees with n edges and having nonleaf nodes 
of outdegree 0 or 1. - 
Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 03 2002

I tried to contact him without success.
Has anybody a clue?

My problems origin mainly in the expression "non-leaf nodes of
outdegree 0": these are leaves or I am an idiot (of course, both
statements are possibly true but one of them should not be false).

Roland Bacher


A071879 		Coefficients of power series solution to g(x) = 1 + x*g(x) + (x*g(x))^3. The first-order differences of these coefficients of g(x), where: g(x) = 1 + 1x + 1x^2 + 2x^3 + 5x^4 + 11x^5 + 24x^6 + ... + a(n)*x^n + ..., forms the coefficients of the third power of g(x), where: g(x)^3 = 1 + 3x + 6x^2 + 13x^3 + 33x^4 + 84x^5 + 208x^6 + 522x^7 + ... 		+20
2
	1, 1, 1, 2, 5, 11, 24, 57, 141, 349, 871, 2212, 5688, 14730, 38403, 100829, 266333, 706997, 1885165, 5047522, 13565203, 36578497, 98934826, 268342933, 729709432, 1989021256, 5433518806, 14873285506, 40790118487, 112064912455 (list; graph; listen)
	OFFSET 	

0,4
	
	COMMENT 	

Number of ordered trees with n edges and having nonleaf nodes of outdegree 0 or 1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 03 2002

G.f. (offset 1) is series reversion of x^2/(x+x^2+x^4).