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A318148
Coefficients of the Omega polynomials of order 4, triangle T(n,k) read by rows with 0<=k<=n.
2
1, 0, 1, 0, -34, 35, 0, 11056, -16830, 5775, 0, -14873104, 27560780, -15315300, 2627625, 0, 56814228736, -119412815760, 84786627900, -24734209500, 2546168625, 0, -495812444583424, 1140896479608800, -948030209181000, 364143337057500, -65706427536750, 4509264634875
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.
T(n,1) ~ A273352(n), T(n,n) = A025036(n).
A023531 (m=1), A318146 (m=2), A318147 (m=3), this seq (m=4).
Sequence in context: A204773 A291512 A165855 * A271984 A254756 A203462
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Aug 22 2018
STATUS
approved