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 A213735 #22 May 14 2025 09:08:51 %S A213735 1,1,-1,1,-3,1,1,-6,7,-1,1,-10,25,-15,1,1,-15,65,-90,31,-1,1,-21,140, %T A213735 -350,301,-63,1,1,-28,266,-1050,1701,-966,127,-1,1,-36,462,-2646,6951, %U A213735 -7770,3025,-255,1,1,-45,750,-5880,22827,-42525,34105,-9330,511,-1 %N A213735 Triangle read by rows: row n is the expansion of x^n in terms of (x+k)!/x! for decreasing k. %C A213735 Signed version of A008278. %e A213735 Triangle starts %e A213735 1; %e A213735 1, -1; %e A213735 1, -3, 1; %e A213735 1, -6, 7, -1; %e A213735 1, -10, 25, -15, 1; %e A213735 1, -15, 65, -90, 31, -1; %e A213735 ... %e A213735 The fourth row corresponds to the expansion x^3 = 1*(x + 3)!/x! - 6*(x + 2)!/x! + 7*(x + 1)!/x! - 1. %o A213735 (Maxima) f1(p, n) := if n = 0 then [p] else [coeff(p, x ^ n), f1(p - expand(product(x + i, i, 1, n) * coeff(p, x^ n)), n - 1)]$ %o A213735 f(n) := flatten(f1(x ^ n, n))$ %K A213735 sign,tabl %O A213735 0,5 %A A213735 _Douglas Boffey_, Jun 18 2012