A318148 - OEIS

%I #10 Aug 26 2018 05:31:09

%S 1,0,1,0,-34,35,0,11056,-16830,5775,0,-14873104,27560780,-15315300,

%T 2627625,0,56814228736,-119412815760,84786627900,-24734209500,

%U 2546168625,0,-495812444583424,1140896479608800,-948030209181000,364143337057500,-65706427536750,4509264634875

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

%C The name 'Omega polynomial' is not a standard name.

%F 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).

%e [0] [1]

%e [1] [0,           1]

%e [2] [0,         -34,            35]

%e [3] [0,       11056,        -16830,        5775]

%e [4] [0,   -14873104,      27560780,   -15315300,      2627625]

%e [5] [0, 56814228736, -119412815760, 84786627900, -24734209500, 2546168625]

%p # See A318146 for the missing functions.

%p FL([seq(CL(OmegaPolynomial(4, n)), n=0..8)]);

%t (* OmegaPolynomials are defined in A318146 *)

%t Table[CoefficientList[OmegaPolynomial[4, n], x], {n, 0, 6}] // Flatten

%o (Sage)

%o # See A318146 for the function OmegaPolynomial.

%o [list(OmegaPolynomial(4, n)) for n in (0..6)]

%Y All row sums are 1, alternating row sums (taken absolute) are A211212.

%Y T(n,1) ~ A273352(n), T(n,n) = A025036(n).

%Y A023531 (m=1), A318146 (m=2), A318147 (m=3), this seq (m=4).

%K sign,tabl

%O 0,5

%A _Peter Luschny_, Aug 22 2018