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 A343233 #23 Mar 22 2025 02:13:13
%S A343233 1,-1,1,-1,-1,1,-2,-1,-1,1,-5,-2,-1,-1,1,-14,-5,-2,-1,-1,1,-42,-14,-5,
%T A343233 -2,-1,-1,1,-132,-42,-14,-5,-2,-1,-1,1,-429,-132,-42,-14,-5,-2,-1,-1,
%U A343233 1,-1430,-429,-132,-42,-14,-5,-2,-1,-1,1
%N A343233 Triangle read by rows: Riordan triangle T = (1 - x*c(x), x), with the generating function c of A000108 (Catalan).
%C A343233 As an unsigned sequence a(n) this is identical with the one of A155586(n+1), for n >= 0, but the triangle is not a simple signed version of A155586. See the formula.
%C A343233 This lower triangular Riordan matrix T of Toeplitz type is the inverse of the Riordan matrix (c(x), x) = |A106270|, also of Toeplitz type.
%F A343233 The lower triangular matrix T satisfies: T = I - L^{tr}*|A106270|, also for the finite N X N version, with the unit matrix I and the lower triangular matrix L^{tr}(i, j) = delta_{i, j-1} (Kronecker symbol delta) with first lower diagonal of 1s and 0 otherwise.
%F A343233 T(n, n) = 1, and for T(n, m) = -C_{n - 1 - m } = - |A106270(n-1, m)|, for 0 <= m <= n-1, with the Catalan numbers C(n) = A000108, and T(n, m) = 0 for n < m.
%F A343233 O.g.f. of column m: (1/c(x))*x^m = (1 - x*c(x))*x^m (Riordan matrix of Toeplitz type), with the o.g.f. c of A000108.
%F A343233 O.g.f. row polynomials R(n, x) = Sum_{m=0..n} T(n, m)*x^m, that is the o.g.f. of the triangle. G(z, x) = c(z)/(1 - x*z).
%e A343233 The triangle matrix T begins:
%e A343233 n/m 0 1 2 3 4 5 6 7 8 9 ...
%e A343233 --------------------------------------------------
%e A343233 0: 1
%e A343233 1: -1 1
%e A343233 2: -1 -1 1
%e A343233 3: -2 -1 -1 1
%e A343233 4: -5 -2 -1 -1 1
%e A343233 5: -14 -5 -2 -1 -1 1
%e A343233 6: -42 -14 -5 -2 -1 -1 1
%e A343233 7: -132 -42 -14 -5 -2 -1 -1 1
%e A343233 8: -429 -132 -42 -14 -5 -2 -1 -1 1
%e A343233 9: -1430 -429 -132 -42 -14 -5 -2 -1 -1 1
%e A343233 ...
%Y A343233 Cf. A106270 (unsigned), A155586.
%K A343233 sign,tabl,easy
%O A343233 0,7
%A A343233 _Gary W. Adamson_ and _Wolfdieter Lang_, Apr 12 2021