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 A116855 #18 May 04 2024 09:24:15 %S A116855 1,1,1,1,2,1,1,2,3,1,1,2,6,4,1,1,2,6,13,5,1,1,2,6,24,23,6,1,1,2,6,24, %T A116855 67,36,7,1,1,2,6,24,120,146,52,8,1,1,2,6,24,120,411,272,71,9,1,1,2,6, %U A116855 24,120,720,1067,456,93,10,1 %N A116855 Triangle read by rows, constructed from binomial transforms of prefixes of A000255 (see Comments for precise definition). %C A116855 Form a matrix R whose columns are [1,0,0,0,...], [1,1,0,0,0,...], [1,1,3,0,0,0,...], [1,1,3,11,0,0,0,...], [1,1,3,11,53,0,0,0,...], ..., formed from the prefixes of A000255 each padded with infinitely many zeros. %C A116855 Replace each column of R by its binomial transform to get the matrix S. %C A116855 Rows converge to sequence A000142 of factorial numbers. %e A116855 The first few rows of S are %e A116855 1, 1, 1, 1, ... %e A116855 1, 2, 3, 4, ... %e A116855 1, 2, 6, 13, ... %e A116855 1, 2, 6, 24, ... %e A116855 ... %e A116855 Read S by antidiagonals to get the desired triangle, which begins %e A116855 1; %e A116855 1, 1; %e A116855 1, 2, 1; %e A116855 1, 2, 3, 1; %e A116855 1, 2, 6, 4, 1; %e A116855 1, 2, 6, 13, 5, 1; %e A116855 1, 2, 6, 24, 23, 6, 1; %e A116855 1, 2, 6, 24, 67, 36, 7, 1; %e A116855 ... %Y A116855 Cf. A000255, A010027. %K A116855 nonn,tabl %O A116855 1,5 %A A116855 _Gary W. Adamson_, Feb 24 2006 %E A116855 Edited by _N. J. A. Sloane_, Aug 11 2019