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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). 2

%I

%S -4,4,8,2,-10,0,12,0,16,-32,-16,32,-4,-4,120,-120,-120,120,0,-96,-96,

%T 960,-480,-864,576,80,80,-1680,-1680,8400,-1680,-6720,3360,0,3840,

%U 3840,-26880,-26880,80640,0,-57600,23040,-6048,-6048,120960,120960,-423360,-423360,846720,120960,-544320,181440

%N 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 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 Row sums are {8, 4, 0, -8, 0, 160, 0, -12096, 0, 2419200, 0,....}.

%D Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965, pp 296-298

%H G. C. Greubel, <a href="/A176295/b176295.txt">Rows n = 0..100 of triangle, flattened</a>

%e Triangle begins as:

%e -4, 4, 8;

%e 2, -10, 0, 12;

%e 0, 16, -32, -16, 32;

%e -4, -4, 120, -120, -120, 120;

%e 0, -96, -96, 960, -480, -864, 576;

%e 80, 80, -1680, -1680, 8400, -1680, -6720, 3360;

%e 0, 3840, 3840, -26880, -26880, 80640, 0, -57600, 23040;

%t 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 Cf. A048998, A138133 (the first part of the expansion).

%K sign,tabf

%O 0,1

%A _Roger L. Bagula_, Dec 07 2010

%E Edited by _N. J. A. Sloane_, Jan 01 2011

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)