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 A206022 #12 Dec 25 2023 18:14:26 %S A206022 1,0,1,0,-2,1,0,2,-4,1,0,0,8,-6,1,0,-2,-8,18,-8,1,0,0,0,-32,32,-10,1, %T A206022 0,4,8,30,-80,50,-12,1,0,0,0,0,128,-160,72,-14,1,0,-10,-16,-28,-112, %U A206022 350,-280,98,-16,1,0,0,0 %N A206022 Riordan array (1, x*exp(arcsinh(-2*x))). %C A206022 Riordan array (1, x*(sqrt(1+4x^2)-2x)); inverse of Riordan array (1, x/sqrt(1-4x)), see A205813. %C A206022 The g.f. for row sums (1,1,-1,-1,3,1,-9,1,27,13,-81,67,243,...) is (1+2*x^2+x*sqrt(1+4*x^2))/(1+3*x^2). %C A206022 Triangle T(n,k), read by rows, given by (0, -2, 1, -1, 1, -1, 1, -1, 1, -1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. %F A206022 T(n,n) = 1, T(n+1,n) = -2n = -A005843(n), T(n+2,n) = 2*n^2 = A001105(n), T(n+3,n) = -A130809(n+1), T(2n,n) = A009117(n), T(2n+3,1) = (-1)^n*2*A000108(n). %F A206022 T(n,k) = T(n-2,k-2) - 4*T(n-2,k-1), for k >= 2. %e A206022 Triangle begins: %e A206022 1 %e A206022 0, 1 %e A206022 0, -2, 1 %e A206022 0, 2, -4, 1 %e A206022 0, 0, 8, -6, 1, %e A206022 0, -2, -8, 18, -8, 1 %e A206022 0, 0, 0, -32, 32, -10, 1 %e A206022 0, 4, 8, 30, -80, 50, -12, 1 %e A206022 0, 0, 0, 0, 128, -160, 72, -14, 1 %e A206022 0, -10, -16, -28, -112, 350, -280, 98, -16, 1 %e A206022 0, 0, 0, 0, 0, -512, 768, -448, 128, -18, 1 %e A206022 0, 28, 40, 54, 96, 420, -1512, 1470, -672, 162, -20, 1 %Y A206022 Cf. A104624 (column k=1). %K A206022 easy,sign,tabl %O A206022 0,5 %A A206022 _Philippe Deléham_, Feb 02 2012