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A176295
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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).
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2
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-4, 4, 8, 2, -10, 0, 12, 0, 16, -32, -16, 32, -4, -4, 120, -120, -120, 120, 0, -96, -96, 960, -480, -864, 576, 80, 80, -1680, -1680, 8400, -1680, -6720, 3360, 0, 3840, 3840, -26880, -26880, 80640, 0, -57600, 23040, -6048, -6048, 120960, 120960, -423360, -423360, 846720, 120960, -544320, 181440
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OFFSET
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0,1
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COMMENTS
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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.
Row sums are {8, 4, 0, -8, 0, 160, 0, -12096, 0, 2419200, 0,....}.
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REFERENCES
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Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965, pp 296-298
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LINKS
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EXAMPLE
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Triangle begins as:
-4, 4, 8;
2, -10, 0, 12;
0, 16, -32, -16, 32;
-4, -4, 120, -120, -120, 120;
0, -96, -96, 960, -480, -864, 576;
80, 80, -1680, -1680, 8400, -1680, -6720, 3360;
0, 3840, 3840, -26880, -26880, 80640, 0, -57600, 23040;
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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