OFFSET
0,5
COMMENTS
The name 'Omega polynomial' is not a standard name.
FORMULA
Omega(m, n, z) = (m*n)!*[z^(n*m)] H(m, z)^x where H(m, z) = hypergeom([], [seq(i/m, i=1..m-1)], (z/m)^m). We consider here the case m = 4 (for other cases see the cross-references).
EXAMPLE
[0] [1]
[1] [0, 1]
[2] [0, -34, 35]
[3] [0, 11056, -16830, 5775]
[4] [0, -14873104, 27560780, -15315300, 2627625]
[5] [0, 56814228736, -119412815760, 84786627900, -24734209500, 2546168625]
MAPLE
# See A318146 for the missing functions.
FL([seq(CL(OmegaPolynomial(4, n)), n=0..8)]);
MATHEMATICA
(* OmegaPolynomials are defined in A318146 *)
Table[CoefficientList[OmegaPolynomial[4, n], x], {n, 0, 6}] // Flatten
PROG
(Sage)
# See A318146 for the function OmegaPolynomial.
[list(OmegaPolynomial(4, n)) for n in (0..6)]
CROSSREFS
All row sums are 1, alternating row sums (taken absolute) are A211212.
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Aug 22 2018
STATUS
approved