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%I #14 Mar 09 2022 08:00:54
%S 1,0,1,1,2,1,0,3,4,1,1,4,9,6,1,0,5,16,19,8,1,1,6,25,44,33,10,1,0,7,36,
%T 85,96,51,12,1,1,8,49,146,225,180,73,14,1,0,9,64,231,456,501,304,99,
%U 16,1,1,10,81,344,833,1182,985,476,129,18,1,0,11,100,489,1408,2471,2668
%N Riordan array (1/(1-x^2), x(1+x)/(1-x)).
%F Columns are generated by x^k*(1+x)^(k-1)/(1-x)^(k+1).
%F T(n, k) = Sum_{j=0..n-k} C(k-1, j)*C(n-j, n-k-j).
%F T(n, k) = (n - k + 1)*hypergeom([1 - k, k - n], [2], 2). - _Peter Luschny_, Mar 09 2022
%e Rows start
%e 1;
%e 0, 1;
%e 1, 2, 1;
%e 0, 3, 4, 1;
%e 1, 4, 9, 6, 1;
%e 0, 5, 16, 19, 8, 1;
%t t[n_, k_] := Binomial[n+k, k]*Hypergeometric2F1[-k+1, -n, -n-k, -1]; Table[t[n-k, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Nov 22 2013 *)
%Y Cf. A119328 (row-reversed).
%Y Row sums are A097076(n+1).
%Y Diagonal sums are abs(A077902).
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Dec 08 2004
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