%I #14 Feb 12 2024 08:41:27
%S 1,0,1,-1,1,1,-48,28,25,-1,233280,-91368,-60993,2305,1,222953472000,
%T -65503641600,-33198846720,985867696,446161,-1,-69132994560000000000,
%U 16249035196800000000,6593300559405000000,-157196644177875000,-59060479175425,144069601,1
%N Characteristic polynomials of the inverse beta function based matrices as a triangle of integer coefficients: n*IM(i,j) = n*Inverse(1/Gamma(i,j)); i,j>=n.
%H Roger L. Bagula, <a href="/A136455/b136455.txt">Table of n, a(n) for n = 1..78</a>
%F M(i,j)=1/Gamma[i+j]; i,j<=n IM(i,j)=Inverse(M(i,j))
%e {1},
%e {0, 1},
%e {-1, 1, 1},
%e {-48, 28, 25, -1},
%e {233280, -91368, -60993, 2305, 1},
%e {222953472000, -65503641600, -33198846720, 985867696, 446161, -1}
%t M[w_] := Table[Table[1/Gamma[n + m], {n, 0, w}], {m, 0, w}]
%t IM[w_] := Inverse[M[w]] Join[{1, x}, Table[CharacteristicPolynomial[n*IM[n], x], {n, 1, 10}]]
%t a = Join[{{1}, {0,1}}, Table[CoefficientList[CharacteristicPolynomial[n*IM[n], x], x], {n, 1, 10}]];
%t Flatten[a]
%t Join[{1, 1}, Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[n*IM[n], x], x]], {n, 1, 10}]]
%K uned,tabl,sign
%O 1,7
%A _Roger L. Bagula_, Mar 20 2008