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 = 3 (for other cases see the cross-references).
EXAMPLE
[0] [1]
[1] [0, 1]
[2] [0, -9, 10]
[3] [0, 477, -756, 280]
[4] [0, -74601, 142362, -83160, 15400]
[5] [0, 25740261, -55429920, 40900860, -12612600, 1401400]
[6] [0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400,190590400]
MAPLE
# See A318146 for the missing functions.
FL([seq(CL(OmegaPolynomial(3, n)), n=0..8)]);
MATHEMATICA
(* OmegaPolynomials are defined in A318146 *)
Table[CoefficientList[OmegaPolynomial[3, n], x], {n, 0, 6}] // Flatten
PROG
(Sage)
# See A318146 for the function OmegaPolynomial.
[list(OmegaPolynomial(3, n)) for n in (0..6)]
CROSSREFS
All row sums are 1, alternating row sums (taken absolute) are A002115.
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Aug 22 2018
STATUS
approved