%I A064580
%S A064580 1,1,1,1,2,2,1,3,5,5,1,4,9,14,13,1,5,14,28,40,36,1,6,20,48,87,118,104,
%T A064580 1,7,27,75,161,273,357,309,1,8,35,110,270,536,866,1100,939,1,9,44,154,
%U A064580 423,951,1782,2772,3441,2905,1,10,54,208,630,1572,3310,5928,8946,10900
%N A064580 Triangle associated with rooted trees with a degree constraint (A036765).
%C A064580 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 21 2009: 
               (Start)
%C A064580 Row sums = A161898: (1, 2, 5, 14, 41, 124, 384,...).
%C A064580 Right border = A136751.
%C A064580 Reversal of the triangle = a convergent of infinite products a*b*c,...
%C A064580 of "aerate and multiply" where a = A007318, b = A007318 interleaved with 
               zeros
%C A064580 (by columns), c = A007318 interleaved with two adjacent zeros, and so 
               on. (End)
%F A064580 a(n, k)=a(n-1, k)+a(n-1, k-1)+a(n-1, k-2)+a(n-1, k-3) with a(0, 0)=1 
               and a(n, k)=0 if n<k or k<0.
%Y A064580 Columns include A000012, A000027, A000096. Right hand column is A036765. 
               The sequence of triangles A010054 (Triangle Indicator), A007318 (Pascal), 
               A026300 (Motzkin), A064580, ... converges to the triangle A009766 
               (Catalan).
%Y A064580 A161898, A136751 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 21 
               2009]
%Y A064580 Sequence in context: A099514 A139687 A064581 this_sequence A009766 A059718 
               A076038
%Y A064580 Adjacent sequences: A064577 A064578 A064579 this_sequence A064581 A064582 
               A064583
%K A064580 nonn,tabl
%O A064580 0,5
%A A064580 Henry Bottomley (se16(AT)btinternet.com), Sep 21 2001
%E A064580 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggsetion 
               of Andrew Plewe, Jun 17 2007