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A176295 Triangle read by rows, based on the two-variable g.f. exp(x*t)*(x*(1 - 2*exp(x)) - 2*exp(x))/(1 - exp(t)) (the second of two parts).

%I A176295 #16 Nov 26 2019 04:24:44
%S A176295 -4,4,8,2,-10,0,12,0,16,-32,-16,32,-4,-4,120,-120,-120,120,0,-96,-96,
%T A176295 960,-480,-864,576,80,80,-1680,-1680,8400,-1680,-6720,3360,0,3840,
%U A176295 3840,-26880,-26880,80640,0,-57600,23040,-6048,-6048,120960,120960,-423360,-423360,846720,120960,-544320,181440
%N A176295 Triangle read by rows, based on the two-variable g.f. exp(x*t)*(x*(1 - 2*exp(x)) - 2*exp(x))/(1 - exp(t)) (the second of two parts).
%C A176295 A factor of 2*n!*(n+2)! was used to make the expansion coefficients all integers. This part is the b(i) part of the  Sum_{j=0..n} (a(i) + b(i)*Exp(x) )*x^i, expansion.
%C A176295 Row sums are {8, 4, 0, -8, 0, 160, 0, -12096, 0, 2419200, 0,....}.
%D A176295 Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965, pp 296-298
%H A176295 G. C. Greubel, <a href="/A176295/b176295.txt">Rows n = 0..100 of triangle, flattened</a>
%e A176295 Triangle begins as:
%e A176295   -4,    4,     8;
%e A176295    2,  -10,     0,     12;
%e A176295    0,   16,   -32,    -16,     32;
%e A176295   -4,   -4,   120,   -120,   -120,   120;
%e A176295    0,  -96,   -96,    960,   -480,  -864,   576;
%e A176295   80,   80, -1680,  -1680,   8400, -1680, -6720,   3360;
%e A176295    0, 3840,  3840, -26880, -26880, 80640,     0, -57600, 23040;
%t A176295 p[t_]:= Exp[x*t]*(x*(1 -2*Exp[x]) -2*Exp[x])/(1-Exp[t]); Table[Im[ CoefficientList[2*n!*(n+2)!*SeriesCoefficient[Series[p[t], {t,0,30}]/.Exp[x] -> I, n], x]], {n,0,12}]//Flatten
%Y A176295 Cf. A048998, A138133 (the first part of the expansion).
%K A176295 sign,tabf
%O A176295 0,1
%A A176295 _Roger L. Bagula_, Dec 07 2010
%E A176295 Edited by _N. J. A. Sloane_, Jan 01 2011