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.
0; -1, 1; -1, 0, -1; -1, 0, 0, 1; -1, 4, 0, 4, -1; -1, 5, 0, 0, -5,1; -1, 6, -15, 0, -15, 6, -1; -1, 7, -21, 0, 0, 21, -7, 1; -1, 8, -28, 56, 0,56, -28, 8, -1; -1, 9, -36, 84, 0, 0, -84, 36, -9, 1; -1, 10, -45, 120, -210, 0, -210, 120, -45, 10, -1;
A140574 := proc(n,k) if abs(k-n/2) < 1 and not n= 1 then 0; else (-1)^(k+1)*binomial(n,k) ; end if; end proc: seq(seq(A140574(n,m),m=0..n),n=0..14) ; # R. J. Mathar, Nov 10 2011
Clear[p, f, x, n] f[x_, n_] := (-1)^ Floor[n/2]*If [Mod[n, 2] == 1, Binomial[n, Floor[n/2]]*x^( Floor[n/2]) - Binomial[n, Floor[n/2] + 1]*x^(Floor[n/2] + 1), Binomial[n, Floor[n/2]]*x^(Floor[n/2])]; p[x, 0] = 0; p[x, 1] = 1 - x; p[x_, n_] := p[x, n] = f[x, n] - (1 - x)^n; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]
0; 2, -1; 0, 2, -1; 2, -3, 3, -1; 0, 4, -6, 4, -1; 2, -5, 10, -10, 5, -1; 0, 6, -15, 20, -15, 6, -1; 2, -7, 21, -35, 35, -21, 7, -1; 0, 8, -28,56, -70, 56, -28, 8, -1; 2, -9, 36, -84, 126, -126, 84, -36, 9, -1; 0, 10, -45, 120, -210, 252, -210, 120, -45, 10, -1;
Clear[p] p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := x^n*(1/x^n - (1 - 1/x)^n); a = Table[ExpandAll[p[x, n]], {n, 0, 10}]; b = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}]; Flatten[b]
Comments