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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
-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
OFFSET
0,1
COMMENTS
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,....}.
REFERENCES
Frederick T. Wall, Chemical Thermodynamics, W. H. Freeman, San Francisco, 1965, pp 296-298
EXAMPLE
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;
MATHEMATICA
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
CROSSREFS
Cf. A048998, A138133 (the first part of the expansion).
Sequence in context: A091671 A137797 A358561 * A140874 A355234 A021227
KEYWORD
sign,tabf
AUTHOR
Roger L. Bagula, Dec 07 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jan 01 2011
STATUS
approved