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.
{a(n)=sum(k=0,n,k!*abs((matrix(n+1,n+1,r,c,if(r>=c,(r-c)!* sum(m=0,r-c+1,(-1)^(r-c+1-m)*m^r/m!/(r-c+1-m)!)))^-1)[n+1,k+1]))}
Triangle T begins: 1; -1,1; 1,-3,1; -1,9,-7,1; 1,-45,55,-15,1; -1,585,-835,285,-31,1; 1,-21105,30835,-11025,1351,-63,1; -1,1858185,-2719675,977445,-121891,6069,-127,1; 1,-367958745,538607755,-193649085,24187051,-1213065,26335,-255,1; ... Matrix inverse begins: 1; 1,1; 2,3,1; 6,12,7,1; 24,60,50,15,1; 120,360,390,180,31,1; ... where [T^-1](n,k) = (n-k)!*A008278(n+1,k+1).
rows = 10;
M = Table[If[r >= c, (r-c)! Sum[(-1)^(r-c-m+1) m^r/m!/(r-c-m+1)!, {m, 0, r-c+1}], 0], {r, rows}, {c, rows}] // Inverse;
T[n_, k_] := M[[n+1, k+1]];
Table[T[n, k], {n, 0, rows-1}, {k, 0, n}] (* Jean-François Alcover, Jun 27 2019, from PARI *)
{T(n,k)=(matrix(n+1,n+1,r,c,if(r>=c,(r-c)!* sum(m=0,r-c+1,(-1)^(r-c+1-m)*m^r/m!/(r-c+1-m)!)))^-1)[n+1,k+1]}
def A106340_matrix(d): def A130850(n, k): # EulerianNumber = A173018 return add(EulerianNumber(n,j)*binomial(n-j,k) for j in (0..n)) return matrix(ZZ, d, A130850).inverse() A106340_matrix(8) # Peter Luschny, May 21 2013
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