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%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
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