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.
r = (1 - 2z^2 - Sqrt[1-4z^2]) / (2z^2);
gf = (r^2 z + r u^2 + r u + 2 r z + z) / (z (1 - r u));
Table[SeriesCoefficient[gf,{u,0,1},{z,0,n}], {n,0,50}] (* Andrei Zabolotskii, Jul 25 2025 *)
Triangle begins 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 3, 1, 1, 5, 5, 4, 4, 1, 1, 5, 9, 9, 5, 5, 1, 1, 14, 14, 14, 14, 6, 6, 1, 1, 14, 28, 28, 20, 20, 7, 7, 1, 1, 42, 42, 48, 48, 27, 27, 8, 8, 1, 1 The production array of this matrix begins 1, 1, 0, 0, 1, 1, 1, 0, 1, -1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1
(* The function RiordanArray is defined in A256893. *) nmax = 10; M = PadRight[#, nmax+1]& /@ RiordanArray[(1-#)/(1-#^4)&, #/(1+#^2)&, nmax+1]; T = Inverse[M]; Table[T[[n+1, k+1]], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 16 2019 *)
# Algorithm of L. Seidel (1877) # Prints the first n rows of the signed version of the triangle. def Signed_A165621_triangle(n) : D = [0]*(n+4); D[1] = 1 b = False; h = 3 for i in range(2*n) : if b : for k in range(h,0,-1) : D[k] += D[k-1] h += 1 else : for k in range(1,h, 1) : D[k] -= D[k+1] if b : print([D[z] for z in (2..h-2)]) b = not b Signed_A165621_triangle(11) # Peter Luschny, May 01 2012
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