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 A269949 #24 Aug 13 2021 13:50:42
%S A269949 1,1,1,3,3,1,5,15,5,1,35,35,35,7,1,63,315,105,63,9,1,231,693,1155,231,
%T A269949 99,11,1,429,3003,3003,3003,429,143,13,1,6435,6435,15015,9009,6435,
%U A269949 715,195,15,1,12155,109395,36465,51051,21879,12155,1105,255,17,1
%N A269949 Triangle read by rows, T(n,k) = denominator(binomial(-1/2, n-k))*binomial(n-1/2, k-1/2), for n>=0 and 0<=k<=n.
%C A269949 Numerators of "gravitational descendent fields" presented on p. 28 of the Zhou reference. See also p. 31. - _Tom Copeland_, Feb 13 2017
%H A269949 J. Zhou, <a href="http://arxiv.org/abs/1405.5296">Quantum deformation theory of the Airy curve and the mirror symmetry of a point</a>, arXiv preprint arXiv:1405.5296 [math.AG], 2014.
%e A269949 Triangle starts:
%e A269949 [ 1]
%e A269949 [ 1, 1]
%e A269949 [ 3, 3, 1]
%e A269949 [ 5, 15, 5, 1]
%e A269949 [ 35, 35, 35, 7, 1]
%e A269949 [ 63, 315, 105, 63, 9, 1]
%e A269949 [231, 693, 1155, 231, 99, 11, 1]
%t A269949 Table[Denominator[Binomial[-1/2, n - k]] Binomial[n - 1/2, k - 1/2], {n, 0, 9}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Feb 13 2017 *)
%o A269949 (Sage)
%o A269949 A269949 = lambda n,k: binomial(-1/2,n-k).denom()*binomial(n-1/2,k-1/2)
%o A269949 for n in range(8): print([A269949(n,k) for k in (0..n)])
%Y A269949 Cf. A001790 (col. 0), A001803 (col. 1), A161199 (col. 2), A161201 (col. 3).
%Y A269949 Cf. A269950.
%K A269949 nonn,tabl
%O A269949 0,4
%A A269949 _Peter Luschny_, Apr 07 2016