A136455 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.

1, 0, 1, -1, 1, 1, -48, 28, 25, -1, 233280, -91368, -60993, 2305, 1, 222953472000, -65503641600, -33198846720, 985867696, 446161, -1, -69132994560000000000, 16249035196800000000, 6593300559405000000, -157196644177875000, -59060479175425, 144069601, 1

Offset

1,7

Links

Roger L. Bagula, Table of n, a(n) for n = 1..78

Formula

M(i,j)=1/Gamma[i+j]; i,j<=n IM(i,j)=Inverse(M(i,j))

Example

{1},
{0, 1},
{-1, 1, 1},
{-48, 28, 25, -1},
{233280, -91368, -60993, 2305, 1},
{222953472000, -65503641600, -33198846720, 985867696, 446161, -1}

Mathematica

M[w_] := Table[Table[1/Gamma[n + m], {n, 0, w}], {m, 0, w}]
IM[w_] := Inverse[M[w]] Join[{1, x}, Table[CharacteristicPolynomial[n*IM[n], x], {n, 1, 10}]]
a = Join[{{1}, {0, 1}}, Table[CoefficientList[CharacteristicPolynomial[n*IM[n], x], x], {n, 1, 10}]];
Flatten[a]
Join[{1, 1}, Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[n*IM[n], x], x]], {n, 1, 10}]]

Crossrefs

Sequence in context: A128380 A298451 A094658 * A085517 A299525 A033694

Adjacent sequences: A136452 A136453 A136454 * A136456 A136457 A136458

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Mar 20 2008

Status

approved