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 A165293 #12 Jan 22 2020 04:27:07
%S A165293 1,10,-1,100,-20,1,1000,-300,30,-1,10000,-4000,600,-40,1,100000,
%T A165293 -50000,10000,-1000,50,-1,1000000,-600000,150000,-20000,1500,-60,1,
%U A165293 10000000,-7000000,2100000,-350000,35000,-2100,70
%N A165293 Inverse of A038303, and generalization of A130595.
%C A165293 Rows sum up to A001019 (powers of 9), diagonals to A004189, a generalization of A010892 (the inverse Fibonacci). Ratio of diagonal sums converges to a decimal sequence: A000108 (Catalan numbers), which is the squared difference of sqrt(2) and sqrt(3), or 5-sqrt(24). Ratio between first binomial transform (A054320 and A138288)of A004189, converges to sqrt(2/3). 1/(2*sqrt(24)) gives A000984 (central binomial coefficients) as a decimal sequence.
%C A165293 Triangle T(n,k), read by rows, given by [10,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 15 2009
%F A165293 Sum_{k=0..n} T(n,k)*x^k = (10-x)^n. - _Philippe Deléham_, Dec 15 2009
%F A165293 G.f.: x*y/(1-10*x+x*y). - _R. J. Mathar_, Aug 11 2015
%e A165293 Triangle begins:
%e A165293 1;
%e A165293 10, -1;
%e A165293 100, -20, 1;
%e A165293 1000, -300, 30, -1;
%e A165293 10000, -4000, 600, -40, 1;
%Y A165293 Cf. A007318, A130595, A038303, A004189, A010892, A001079, A054320, A138288, A041041, A000108.
%K A165293 tabl,sign
%O A165293 1,2
%A A165293 _Mark Dols_, Sep 13 2009