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

%I A318148 #10 Aug 26 2018 05:31:09
%S A318148 1,0,1,0,-34,35,0,11056,-16830,5775,0,-14873104,27560780,-15315300,
%T A318148 2627625,0,56814228736,-119412815760,84786627900,-24734209500,
%U A318148 2546168625,0,-495812444583424,1140896479608800,-948030209181000,364143337057500,-65706427536750,4509264634875
%N A318148 Coefficients of the Omega polynomials of order 4, triangle T(n,k) read by rows with 0<=k<=n.
%C A318148 The name 'Omega polynomial' is not a standard name.
%F A318148 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 A318148 [0] [1]
%e A318148 [1] [0,           1]
%e A318148 [2] [0,         -34,            35]
%e A318148 [3] [0,       11056,        -16830,        5775]
%e A318148 [4] [0,   -14873104,      27560780,   -15315300,      2627625]
%e A318148 [5] [0, 56814228736, -119412815760, 84786627900, -24734209500, 2546168625]
%p A318148 # See A318146 for the missing functions.
%p A318148 FL([seq(CL(OmegaPolynomial(4, n)), n=0..8)]);
%t A318148 (* OmegaPolynomials are defined in A318146 *)
%t A318148 Table[CoefficientList[OmegaPolynomial[4, n], x], {n, 0, 6}] // Flatten
%o A318148 (Sage)
%o A318148 # See A318146 for the function OmegaPolynomial.
%o A318148 [list(OmegaPolynomial(4, n)) for n in (0..6)]
%Y A318148 All row sums are 1, alternating row sums (taken absolute) are A211212.
%Y A318148 T(n,1) ~ A273352(n), T(n,n) = A025036(n).
%Y A318148 A023531 (m=1), A318146 (m=2), A318147 (m=3), this seq (m=4).
%K A318148 sign,tabl
%O A318148 0,5
%A A318148 _Peter Luschny_, Aug 22 2018