A098505 - OEIS

%I #10 Aug 30 2024 16:33:06

%S 1,1,1,1,1,1,1,3,3,1,1,2,3,2,1,1,5,5,5,5,1,1,1,5,5,5,1,1,1,7,7,35,35,

%T 7,7,1,1,4,14,28,7,28,14,4,1,1,9,18,42,63,63,42,18,9,1,1,5,45,30,105,

%U 63,105,30,45,5,1,1,11,55,165,165,33,33,165,165,55,11,1,1,3,33,55,495,198

%N Numerators in inverse of a Catalan scaled binomial matrix.

%C Row sums are A098506. Diagonal sums are A098507. Second column is A093527. Third column is A098508. Numerators in the inverse of the signed version of A098474, defined by T(n,k)=(-1)^(n-k)binomial(2k,k)binomial(n,k)/(k+1)

%H Paolo Xausa, <a href="/A098505/b098505.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).

%F T(n, k) = numerator((n+1)*binomial(n, k)/binomial(2n, n)).

%e Rows begin:

%e   1;

%e   1,1;

%e   1,1,1;

%e   1,3,3,1;

%e   1,2,3,2,1;

%e   1,5,5,5,5,1;

%e   ...

%t Table[Numerator[(n + 1)*Binomial[n, k]/Binomial[2*n, n]], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Aug 30 2024 *)

%Y Cf. A098474, A098506, A098507, A098508, A093527.

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Sep 11 2004