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 A175011 #9 Mar 30 2024 23:08:41 %S A175011 1,1,2,1,2,5,1,2,2,16,1,2,2,5,45,1,2,2,2,12,125,1,2,2,2,5,24,341,1,2, %T A175011 2,2,2,12,48,918,1,2,2,2,2,7,18,97,2453,1,2,2,2,2,2,16,28,195,6515 %N A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3, ...). %C A175011 Row sums = A001906, the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...). %F A175011 Given S(x) = (1 + 2x + 3x^2 + ...), where (1, 2, 3, ...) = the INVERTi transform of (1, 3, 8, 21, 55, ...); k-th row of the array = INVERT transform of S(x^k). Take finite differences of array columns starting from the topmost "1"; becoming rows of the triangle. %e A175011 First few rows of the array: %e A175011 1, 3, 8, 21, 55, 144, 377, 987, 2584, ... %e A175011 1, 1, 3, 5, 10, 19, 36, 69, 131, ... %e A175011 1, 1, 1, 3, 5, 7, 12, 21, 34, ... %e A175011 1, 1, 1, 1, 3, 5, 7, 9, 16, ... %e A175011 1, 1, 1, 1, 1, 3, 5, 7, 9, ... %e A175011 1, 1, 1, 1, 1, 1, 3, 5, 7, ... %e A175011 ... %e A175011 Taking finite differences from the bottom to top starting with the last "1" we obtain triangle A175011: %e A175011 1; %e A175011 1, 2; %e A175011 1, 2, 5; %e A175011 1, 2, 2, 16; %e A175011 1, 2, 2, 5, 45; %e A175011 1, 2, 2, 2, 12, 125; %e A175011 1, 2, 2, 2, 5, 24, 341; %e A175011 1, 2, 2, 2, 2, 12, 48, 918; %e A175011 1, 2, 2, 2, 2, 7, 18, 97, 2453; %e A175011 1, 2, 2, 2, 2, 2, 16, 28, 195, 6515; %e A175011 ... %Y A175011 Cf. A001906. %K A175011 nonn,tabl %O A175011 1,3 %A A175011 _Gary W. Adamson_, Apr 03 2010