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A172380 Eigentriangle of Catalan triangle A033184.

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%I A172380 #13 Nov 11 2022 08:06:51
%S A172380 1,0,1,0,1,1,0,2,3,1,0,5,10,6,1,0,14,36,31,10,1,0,42,137,156,75,15,1,
%T A172380 0,132,544,787,510,155,21,1,0,429,2235,4017,3331,1380,287,28,1,0,1430,
%U A172380 9445,20809,21405,11411,3255,490,36,1,0,4862,40876,109486,136921,90665
%N A172380 Eigentriangle of Catalan triangle A033184.
%C A172380 Row sums are A091768.
%C A172380 Production matrix of inverse is matrix with general term (-1)^(n-k+1)C(k,n-k+1).
%C A172380 Diagonal sums are A172382. Product of A033184 and A172380 is the matrix A172381.
%H A172380 Paul Barry, <a href="http://arxiv.org/abs/1107.5490">Invariant number triangles, eigentriangles and Somos-4 sequences</a>, arXiv preprint arXiv:1107.5490 [math.CO], 2011.
%e A172380 Triangle begins
%e A172380   1;
%e A172380   0,    1;
%e A172380   0,    1,    1;
%e A172380   0,    2,    3,     1;
%e A172380   0,    5,   10,     6,     1;
%e A172380   0,   14,   36,    31,    10,     1;
%e A172380   0,   42,  137,   156,    75,    15,    1;
%e A172380   0,  132,  544,   787,   510,   155,   21,   1;
%e A172380   0,  429, 2235,  4017,  3331,  1380,  287,  28,  1;
%e A172380   0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1;
%e A172380 Production matrix of inverse is
%e A172380   0,  1;
%e A172380   0, -1,  1;
%e A172380   0,  0, -2,  1;
%e A172380   0,  0,  1, -3,  1;
%e A172380   0,  0,  0,  3, -4,   1;
%e A172380   0,  0,  0, -1,  6,  -5,   1;
%e A172380   0,  0,  0,  0, -4,  10,  -6,   1;
%e A172380   0,  0,  0,  0,  1, -10,  15,  -7,   1;
%e A172380   0,  0,  0,  0,  0,   5, -20,  21,  -8,  1;
%e A172380   0,  0,  0,  0,  0,  -1,  15, -35,  28, -9,   1;
%e A172380   0,  0,  0,  0,  0,   0,  -6,  35, -56, 36, -10, 1;
%K A172380 nonn,tabl
%O A172380 0,8
%A A172380 _Paul Barry_, Feb 01 2010