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 A326832 #13 Jan 05 2025 19:51:41
%S A326832 1,-3,4,10,-20,11,-35,84,-77,29,126,-336,396,-261,76,-462,1320,-1815,
%T A326832 1595,-836,199,1716,-5148,7865,-8294,5928,-2587,521,-6435,20020,
%U A326832 -33033,39585,-34580,20895,-7815,1364,24310,-77792,136136,-179452,180880,-135320,70856,-23188,3571
%N A326832 Triangle read by rows: T(n, k) = (-1)^(n - k) * binomial(2n + 1, n - k) * L(2k + 1), 0 <= k <= n, where L(k) is the k-th Lucas number (A000032).
%C A326832 This triangle is the subject of the paper by Agarwal (1990).
%H A326832 Ashok Agarwal, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/28-3/agarwal.pdf">On a new kind of numbers</a>, Fibonacci Quarterly, Vol. 28, No. 3 (1990), pp. 194-199.
%H A326832 R. K. Raina and H. M. Srivastava, <a href="https://doi.org/10.1016/S0895-7177(97)00045-9">A class of numbers associated with the Lucas numbers</a>, Mathematical and Computer Modelling, Vol. 25, No. 7 (1997), pp. 15-22.
%F A326832 Sum_{k=0..n} T(n, k) = 1.
%F A326832 T(n + 1, k) = -(2n + 3)*(2n + 2)/((n - k + 1)*(n + k + 2)) * T(n, k).
%t A326832 T[n_, k_] := (-1)^(n - k) * Binomial[2 n + 1, n - k] * LucasL[2 k + 1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
%o A326832 (PARI) L(n) = fibonacci(n+1) + fibonacci(n-1); \\ A000032
%o A326832 T(n, k) = (-1)^(n - k) * binomial(2*n + 1, n - k) * L(2*k + 1); \\ _Michel Marcus_, Oct 21 2019
%Y A326832 Cf. A000032, A007318.
%K A326832 sign,tabl
%O A326832 0,2
%A A326832 _Amiram Eldar_, Oct 20 2019