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A318147 Coefficients of the Omega polynomials of order 3, triangle T(n,k) read by rows with 0<=k<=n.

%I A318147 #11 Aug 26 2018 05:31:02
%S A318147 1,0,1,0,-9,10,0,477,-756,280,0,-74601,142362,-83160,15400,0,25740261,
%T A318147 -55429920,40900860,-12612600,1401400,0,-16591655817,38999319642,
%U A318147 -33465991104,13440707280,-2572970400,190590400
%N A318147 Coefficients of the Omega polynomials of order 3, triangle T(n,k) read by rows with 0<=k<=n.
%C A318147 The name 'Omega polynomial' is not a standard name.
%F A318147 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 = 3 (for other cases see the cross-references).
%e A318147 [0] [1]
%e A318147 [1] [0,            1]
%e A318147 [2] [0,           -9,          10]
%e A318147 [3] [0,          477,        -756,          280]
%e A318147 [4] [0,       -74601,      142362,       -83160,       15400]
%e A318147 [5] [0,     25740261,   -55429920,     40900860,   -12612600,     1401400]
%e A318147 [6] [0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400,190590400]
%p A318147 # See A318146 for the missing functions.
%p A318147 FL([seq(CL(OmegaPolynomial(3, n)), n=0..8)]);
%t A318147 (* OmegaPolynomials are defined in A318146 *)
%t A318147 Table[CoefficientList[OmegaPolynomial[3, n], x], {n, 0, 6}] // Flatten
%o A318147 (Sage)
%o A318147 # See A318146 for the function OmegaPolynomial.
%o A318147 [list(OmegaPolynomial(3, n)) for n in (0..6)]
%Y A318147 All row sums are 1, alternating row sums (taken absolute) are A002115.
%Y A318147 T(n,1) ~ A293951(n), T(n,n) = A025035(n).
%Y A318147 A023531 (m=1), A318146 (m=2), this seq (m=3), A318148 (m=4).
%K A318147 sign,tabl
%O A318147 0,5
%A A318147 _Peter Luschny_, Aug 22 2018