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 A209155 #12 Mar 19 2025 10:08:36 %S A209155 -1,-1,1,-1,3,-1,-1,1,-2,1,-1,5,-5,5,-1,-1,1,-5,5,-3,1,-1,7,-7,35,-7, %T A209155 7,-1,-1,4,-28,7,-14,14,-4,1 %N A209155 Triangle read by rows: numerators of Stirling-like triangle of rational numbers. %C A209155 In Joseph M. Santmyer's paper, Table 1 (A209155/A209156) seems to be incorrect. The paper presents the formula c(n,r) = -(n/(r+1)) * (D(n-1,r-1)/D(n,r)) * c(n-1,r-1) for 1 < r < n-1, where D(n,r) = A323855(n,r). However, in Table 1, the value of c(5,2) is given as -5/3, which does not match the result obtained by applying the formula: -5/3 * D(4,1)/D(5,2) * c(4,1) equals -5. - _Jinyuan Wang_, Mar 17 2025 %H A209155 Joseph M. Santmyer, <a href="http://dx.doi.org/10.1016/S0012-365X(96)00082-9">A Stirling like sequence of rational numbers</a>, Discrete Math. 171 (1997), no. 1-3, 229-235. MR1454453. %e A209155 Triangle begins: %e A209155 -1; %e A209155 -1, 1; %e A209155 -1, 3/2, -1; %e A209155 -1, 1, -2, 1; %e A209155 -1, 5, -5/3, 5/2, -1; %e A209155 -1, 1, -5, 5/2, -3, 1; %e A209155 -1, 7, -7/3, 35/4, -7/2, 7/2, -1; %e A209155 -1, 4, -28/3, 7/3, -14, 14/3, -4, 1; %e A209155 ... %Y A209155 Cf. A209156, A323855. %K A209155 sign,frac,tabl,more %O A209155 1,5 %A A209155 _N. J. A. Sloane_, Mar 05 2012