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%I #13 Nov 11 2022 08:06:51
%S 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 0,132,544,787,510,155,21,1,0,429,2235,4017,3331,1380,287,28,1,0,1430,
%U 9445,20809,21405,11411,3255,490,36,1,0,4862,40876,109486,136921,90665
%N Eigentriangle of Catalan triangle A033184.
%C Row sums are A091768.
%C Production matrix of inverse is matrix with general term (-1)^(n-k+1)C(k,n-k+1).
%C Diagonal sums are A172382. Product of A033184 and A172380 is the matrix A172381.
%H 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 Triangle begins
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 2, 3, 1;
%e 0, 5, 10, 6, 1;
%e 0, 14, 36, 31, 10, 1;
%e 0, 42, 137, 156, 75, 15, 1;
%e 0, 132, 544, 787, 510, 155, 21, 1;
%e 0, 429, 2235, 4017, 3331, 1380, 287, 28, 1;
%e 0, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1;
%e Production matrix of inverse is
%e 0, 1;
%e 0, -1, 1;
%e 0, 0, -2, 1;
%e 0, 0, 1, -3, 1;
%e 0, 0, 0, 3, -4, 1;
%e 0, 0, 0, -1, 6, -5, 1;
%e 0, 0, 0, 0, -4, 10, -6, 1;
%e 0, 0, 0, 0, 1, -10, 15, -7, 1;
%e 0, 0, 0, 0, 0, 5, -20, 21, -8, 1;
%e 0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1;
%e 0, 0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1;
%K nonn,tabl
%O 0,8
%A _Paul Barry_, Feb 01 2010
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