A318148 Coefficients of the Omega polynomials of order 4, triangle T(n,k) read by rows with 0<=k<=n.

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.

Links

Table of n, a(n) for n=0..27.

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

Adjacent sequences: A318145 A318146 A318147 * A318149 A318150 A318151

Keyword

sign,tabl

Author

Peter Luschny, Aug 22 2018

Status

approved