Search: id:A050166
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%I A050166
%S A050166 1,1,2,1,4,5,1,6,14,14,1,8,27,48,42,1,10,44,110,165,132,1,12,65,208,
%T A050166 429,572,429,1,14,90,350,910,1638,2002,1430,1,16,119,544,1700,3808,
%U A050166 6188,7072,4862,1,18,152,798,2907,7752,15504,23256,15194,16796,1,20
%N A050166 Triangle T(n,k)=M(2n,k,-1), 0<=k<=n, n >= 0, array M as in A050144.
%C A050166 Sometimes called Catalan's triangle, although this term is usually reserved 
               for several other triangles!
%C A050166 T is a mirror image of the array in A039598.
%C A050166 Given (1) = row 0, then the sum of terms with alternating signs in row 
               r of A050166 = (-1)^r * A000108(n); where A000108 = 1, 1, 2, 5, 14, 
               42...the Catalan numbers. - Herb Conn, HCR 83, Box 93, Custer, SD 
               57730
%C A050166 The diagonals of this triangle are self-convolutions of the main diagonal 
               A000108(n+1) : 1, 2, 5, 14, 42, 132, 429, . . . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), May 25 2005
%D A050166 B. A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), 
               FAN, Tashkent, 1990, ISBN 5-648-00738-8. English translation published 
               by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; 
               see p. 29.
%D A050166 E. H. M. Brietzke, An identity of Andrews ..., Discrete Math., 308 (2008), 
               4246-4262.
%D A050166 E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 
               241 (2001), 241-265.
%D A050166 A. Nkwanta, Lattice paths and RNA secondary structures, in African Americans 
               in Mathematics, ed. N. Dean, Amer. Math. Soc., 1997, pp. 137-147.
%H A050166 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</
               a>
%F A050166 a(n, k) = C(2n+1, k)*2*(n-k+1)/(2n-k+2) = A039598(n, n-k) = a(n-1, k)+2*a(n-1, 
               k-1)+a(n-1, k-2) [with a(0, 0) = 1 and a(n, k) = 0 if n<0 or n<k]. 
               - Henry Bottomley (se16(AT)btinternet.com), Sep 24 2001
%e A050166 Rows: {1}; {1,2}; {1,4,5}; ...
%Y A050166 Sequence in context: A021983 A161135 A038730 this_sequence A124959 A081281 
               A108198
%Y A050166 Adjacent sequences: A050163 A050164 A050165 this_sequence A050167 A050168 
               A050169
%K A050166 nonn,tabl,easy
%O A050166 0,3
%A A050166 Clark Kimberling (ck6(AT)evansville.edu)
%E A050166 More terms from Larry Reeves (larryr(AT)acm.org), Mar 14 2001

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