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 A143080 #19 Jul 12 2017 21:12:21
%S A143080 1,1,1,6,6,3,1,120,120,60,20,5,1,5040,5040,2520,840,210,42,7,1,362880,
%T A143080 362880,181440,60480,15120,3024,504,72,9,1,39916800,39916800,19958400,
%U A143080 6652800,1663200,332640,55440,7920,990,110,11,1,6227020800,6227020800
%N A143080 Triangular sequence of coefficients from an exponential based polynomial: p(x,n)=If[n == 0, 1, -(2*n - 1)!*x^(2*n)*(Sum[x^i/(i + 2*n)!, {i, 0, Infinity}] - Exp[x]/x^(2*n))].
%C A143080 Row sums are: 1, 2, 16, 326, 13700, 986410, 108505112, ...
%C A143080 These polynomials are based on: f(x)=1/(1-x)-exp(x).
%C A143080 The n-th row is the coefficient list of the permanental polynomial of the (2n-1)X(2n-1) matrix consisting entirely of 1's (see latter Mathematica code below). - _John M. Campbell_, Jul 05 2012
%F A143080 p(x,n)=If[n == 0, 1, -(2*n - 1)!*x^(2*n)*(Sum[x^i/(i + 2*n)!, {i, 0, Infinity}] - Exp[x]/x^(2*n))]; t(n,m)=Coefficients(p)x,n)).
%e A143080 {1},
%e A143080 {1, 1},
%e A143080 {6, 6, 3, 1},
%e A143080 {120, 120, 60, 20, 5, 1},
%e A143080 {5040, 5040, 2520, 840, 210, 42, 7, 1},
%e A143080 {362880, 362880, 181440, 60480, 15120, 3024, 504, 72, 9, 1},
%e A143080 {39916800, 39916800, 19958400, 6652800, 1663200, 332640, 55440, 7920, 990, 110, 11, 1},
%e A143080 {6227020800, 6227020800, 3113510400, 1037836800, 259459200, 51891840, 8648640, 1235520, 154440, 17160, 1716, 156, 13, 1}
%t A143080 Clear[f, x, n, a]; f[x_, n_] := f[x, n] = If[n == 0, 1, -(2*n - 1)!*x^(2*n)*(Sum[x^i/(i + 2*n)!, {i, 0, Infinity}] - Exp[x]/x^(2*n))]; a = Table[CoefficientList[FullSimplify[f[x, n]], x], {n, 0, 10}]; Flatten[a]
%t A143080 Permanent[m_List] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; A[q_] := Array[1 &, {q, q}]; Flatten[Table[Abs[CoefficientList[Expand[Permanent[A[2*n-1] - IdentityMatrix[2*n-1]*x]], x]], {n, 6}]] (* _John M. Campbell_, Jul 05 2012 *)
%Y A143080 Cf. A000522, A094587.
%K A143080 nonn,tabf
%O A143080 1,4
%A A143080 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 15 2008