This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A336859 #24 Aug 09 2020 13:39:37
%S A336859 1,1,1,1,3,1,1,9,5,1,1,31,21,7,1,1,121,89,37,9,1,1,515,393,183,57,11,
%T A336859 1,1,2321,1805,897,321,81,13,1,1,10879,8557,4431,1729,511,109,15,1,1,
%U A336859 52465,41585,22149,9161,3001,761,141,17,1,1,258563,206097,112047,48313,17003,4841,1079,177,19,1
%N A336859 Mirror image of triangular array A336858.
%C A336859 This is a mirror image of A336858, which is a shifted version of _J. M. Bergot_'s triangular array first described in A104858.
%F A336859 T(n,k) = A336858(n, n-k) for 0 <= k <= n.
%F A336859 T(n,k) = T(n, k-1) - T(n-1, k-1) - T(n-1, k-2) for 2 <= k <= n with T(n,0) = T(n,n) = 1 for n >= 0 and T(n,1) = A086616(n-1) for n >= 1.
%F A336859 T(2*n,n) = A333090(n).
%F A336859 Sum_{k=0..n} T(n,k) = A104858(n) for n >= 0.
%F A336859 Bivariate o.g.f.: (x*y*(1 + g(x)) + 1 - y)/((1 - x)*(1 - y + x*y + x*y^2)), where g(w) = 2/(1 - w + sqrt(1 - 6*w + w^2)) = o.g.f. of A006318 (large Schroeder numbers).
%F A336859 Bivariate o.g.f.: (2*x*y*q(x) + 1 - y)/((1 - x)*(1 - y + x*y + x*y^2)), where q(w) = 2/(1 + w + sqrt(1 - 6*w + w^2)) = o.g.f. of A001003 (little Schroeder numbers).
%e A336859 Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
%e A336859 1;
%e A336859 1, 1;
%e A336859 1, 3, 1;
%e A336859 1, 9, 5, 1;
%e A336859 1, 31, 21, 7, 1;
%e A336859 1, 121, 89, 37, 9, 1;
%e A336859 1, 515, 393, 183, 57, 11, 1;
%e A336859 1, 2321, 1805, 897, 321, 81, 13, 1;
%e A336859 1, 10879, 8557, 4431, 1729, 511, 109, 15, 1;
%e A336859 ...
%o A336859 (PARI) A000108(n) = binomial(2*n, n)/(n+1);
%o A336859 A086616(n) = sum(k=0, n, binomial(n+k+1, 2*k+1) * A000108(k));
%o A336859 T(n, k) = if ((k==0) || (n==k), 1, if ((n<0) || (k<0), 0, if (k==1, A086616(n-1), if (n>k, T(n, k-1) - T(n-1, k-1) - T(n-1, k-2), 0))));
%o A336859 for(n=0, 10, for (k=0, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Aug 08 2020
%Y A336859 Cf. A001003, A006318, A086616, A104858, A333090, A336858.
%K A336859 nonn,tabl
%O A336859 0,5
%A A336859 _Petros Hadjicostas_, Aug 05 2020