OFFSET
1,4
COMMENTS
Row sums are {1, 0, 0, -2, 0, -24, 80, -720, 5376, -49280, 490752}.
REFERENCES
A. H. W. Beck, Space-Charge Waves and Slow Electromagnetic Waves, Pergamon Press, New York, 1958, page 30
A. M. Kuethe, J. D. Schetzer, Foundations of Aerodynamics, John Wiley and sons, Inc, New York, page 177
FORMULA
p(x,t)=1 - exp(2*x*t)*(t - 1)/(1 + t) = Sum_{n>=0} (P(x,n)*t^n/n!); out_n,m = (n!/2)*Coefficients(P(x,n)).
EXAMPLE
{1},
{-1, 1},
{2, -4, 2},
{-6, 12, -12, 4},
{24, -48, 48, -32, 8},
{-120, 240, -240, 160, -80, 16},
{720, -1440, 1440, -960, 480, -192, 32},
{-5040, 10080, -10080, 6720, -3360, 1344, -448, 64},
{40320, -80640, 80640, -53760, 26880, -10752, 3584, -1024, 128},
{-362880, 725760, -725760, 483840, -241920, 96768, -32256, 9216, -2304, 256}, {3628800, -7257600, 7257600, -4838400, 2419200, -967680, 322560, -92160, 23040, -5120, 512}
MATHEMATICA
p[t_] = FullSimplify[1 - Exp[2*x*t]*(t - 1)/(1 + t)];
g = Table[ ExpandAll[(n!/2)*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];
a = Table[ CoefficientList[(n!/2)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, May 01 2008
STATUS
approved