cp's OEIS Frontend

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.

A209155 Triangle read by rows: numerators of Stirling-like triangle of rational numbers.

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%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