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%I #10 Aug 04 2020 01:40:01
%S 1,1,1,1,1,1,1,2,1,1,1,5,2,1,1,1,14,5,2,1,1,1,42,14,5,2,1,1,1,132,42,
%T 14,5,2,1,1,1,429,132,42,14,5,2,1,1,1,1430,429,132,42,14,5,2,1,1,1,
%U 4862,1430,429,132,42,14,5,2,1,1,1,16796,4862,1430,429,132,42,14,5,2,1,1
%N A modified Catalan sequence array.
%C Row sums are in A155587. Stieltjes associate array to A091491.
%F T(n,k) = [k <= n] * if(k=0, 1, A000108(n-k)) for 0 <= k <= n, where [ ] is the Iverson bracket.
%F Bivariate o.g.f.: 1/(1 - x) + c(x) * x*y/(1 - x*y), where c(x) is the o.g.f. of A000108. - _Petros Hadjicostas_, Aug 03 2020
%e Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 1, 1;
%e 1, 5, 2, 1, 1;
%e 1, 14, 5, 2, 1, 1;
%e 1, 42, 14, 5, 2, 1, 1;
%e 1, 132, 42, 14, 5, 2, 1, 1;
%e 1, 429, 132, 42, 14, 5, 2, 1, 1;
%e 1, 1430, 429, 132, 42, 14, 5, 2, 1, 1;
%e ...
%Y Cf. A000108, A091491, A155587.
%K easy,nonn,tabl
%O 0,8
%A _Paul Barry_, Jan 24 2009
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