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A098509 Denominators of the inverse of a Catalan scaled binomial matrix.

%I A098509 #10 Jan 07 2018 08:10:29
%S A098509 1,1,1,2,1,2,5,5,5,5,14,7,7,7,14,42,42,21,21,42,42,132,22,44,33,44,22,
%T A098509 132,429,429,143,429,429,143,429,429,1430,715,715,715,143,715,715,715,
%U A098509 1430,4862,4862,2431,2431,2431,2431,2431,2431,4862,4862,16796,8398
%N A098509 Denominators of the inverse of a Catalan scaled binomial matrix.
%C A098509 First column and main diagonal are A000108. Row sums are A098510. Diagonal sums are A098511. Second column is A098512.
%F A098509 Triangle T(n, k)=denominator((n+1)binomial(n, k)/binomial(2n, n))
%e A098509 Rows begin
%e A098509 1;
%e A098509 1,1;
%e A098509 2,1,2;
%e A098509 5,5,5,5;
%e A098509 14,7,7,7,14;
%e A098509 ...
%t A098509 T[n_, k_] := Denominator[(n + 1)*(Binomial[n, k]/Binomial[2*n, n])];
%t A098509 Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 07 2018 *)
%Y A098509 Cf. A098505, A098474.
%K A098509 easy,nonn,tabl
%O A098509 0,4
%A A098509 _Paul Barry_, Sep 11 2004