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A216182 Riordan array ((1+x)/(1-x)^2, x(1+x)^2/(1-x)^2).

%I A216182 #13 Nov 19 2021 04:41:41
%S A216182 1,3,1,5,7,1,7,25,11,1,9,63,61,15,1,11,129,231,113,19,1,13,231,681,
%T A216182 575,181,23,1,15,377,1683,2241,1159,265,27,1,17,575,3653,7183,5641,
%U A216182 2047,365,31,1,19,833,7183,19825,22363,11969,3303,481,35,1
%N A216182 Riordan array ((1+x)/(1-x)^2, x(1+x)^2/(1-x)^2).
%C A216182 Triangle formed of odd-numbered columns of the Delannoy triangle A008288.
%H A216182 G. C. Greubel, <a href="/A216182/b216182.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A216182 T(2n, n) = A108448(n+1).
%F A216182 Sum_{k=0..n} T(n,k) = A073717(n+1).
%F A216182 From _G. C. Greubel_, Nov 19 2021: (Start)
%F A216182 T(n, k) = A008288(n+k+1, 2*k+1).
%F A216182 T(n, k) = hypergeometric([-n+k, -2*k-1], [1], 2). (End)
%e A216182 Triangle begins
%e A216182    1;
%e A216182    3,   1;
%e A216182    5,   7,    1;
%e A216182    7,  25,   11,    1;
%e A216182    9,  63,   61,   15,    1;
%e A216182   11, 129,  231,  113,   19,    1;
%e A216182   13, 231,  681,  575,  181,   23,   1;
%e A216182   15, 377, 1683, 2241, 1159,  265,  27,  1;
%e A216182   17, 575, 3653, 7183, 5641, 2047, 365, 31, 1;
%e A216182   ...
%t A216182 A216182[n_, k_]:= Hypergeometric2F1[-n +k, -2*k-1, 1, 2];
%t A216182 Table[A216182[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Nov 19 2021 *)
%o A216182 (Sage)
%o A216182 def A216182(n,k): return simplify( hypergeometric([-n+k, -2*k-1], [1], 2) )
%o A216182 flatten([[A216182(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Nov 19 2021
%Y A216182 Cf. (columns:) A005408, A001845, A001847, A001849, A008419.
%Y A216182 Cf. Diagonals: A000012, A004767, A060820.
%Y A216182 Cf. A008288 (Delannoy triangle), A114123 (even-numbered columns of A008288).
%K A216182 nonn,tabl
%O A216182 0,2
%A A216182 _Philippe Deléham_, Mar 11 2013