\begin{table}%t3
\caption{\label{sechtabla}Coefficients  $a_{r}^{\star} {(i,j)}$ and $ b_{r}^{\star}{(i,j)}$ of
  the power series for $r$, corresponding to a stratified medium with
  a ${\rm sech} ^{2}(Z/{H})$ density distribution.}
\par
%\centerline
{
\small\begin{tabular}{c c l l}
\hline \hline
${i}$  &  ${j}$  &  $a_{r}^{\star} {(i,j)}$     & $ b_{r}^{\star}{(i,j)}$  \\ 
\hline
  1     &  1  &  1  &  1 \\
\hline
  2 & 1 & $-\frac{1}{3} (-1 +\alpha)(1 +\alpha)$ &  $-\frac{2}{3} (-1 +\alpha)(1 +\alpha)$
  \\
    & 2 & $-\frac{1}{3} (1 + 3 \alpha ^{2})$ & $ -1 (1 + \alpha ^{2})$ \\
\hline 
  3 & 1 &   $\frac{2}{15} (-1 +\alpha)^{2}(1 +\alpha)^{2}$  &
  $\frac{17}{45}(-1 +\alpha)^{2}(1 +\alpha)^{2}) $  \\
    & 2 & $\frac{1}{3}(-1 +\alpha)(1 +\alpha)(1 + 3 \alpha ^{2})$ & $\frac{4}{3}
  (-1 +\alpha)(1 +\alpha)(1+ \alpha ^{2})$    \\
    & 3 & $\frac{1}{5} (1 + 10  \alpha ^{2}+ 5 \alpha ^{4})$  &  $\frac{1}{3} (3 +  \alpha ^{2})(1+ 3 \alpha ^{2})$   \\
\hline 
 4 & 1 &   $-\frac{17}{315}(-1 +\alpha)^{3}(1 +\alpha)^{3} $  &  $-\frac{62}{315} (-1 +
  \alpha)^{3}(1 +
  \alpha)^{3}$  \\
    & 2 & $-\frac{11}{45} (-1 +\alpha)^{2}(1 +\alpha)^{2} (1+ 3 \alpha ^{2})$ &
  $-\frac{6}{5} (-1+ \alpha )^{2}(1+ \alpha )^{2} (1 +  \alpha ^{2})$    \\
    & 3 & $-\frac{1}{3}(-1 +\alpha)(1 +\alpha)(1 + 10  \alpha ^{2}+ 5 \alpha ^{4}) $  &
    $-\frac{2}{3}(-1 +\alpha)(1 +\alpha) (3 +\alpha ^{2})(1+ 3 \alpha ^{2})$   \\
    & 4 & $-\frac{1}{7} (1 +21\alpha ^{2}+ 35 \alpha ^{4}+ 7\alpha ^{6} )$ &
    $ -1 (1 + \alpha ^{2})(1+ 6 \alpha ^{2}+  \alpha ^{4} )$ \\
\hline 
 5 & 1 &   $\frac{62}{2835}(-1 +\alpha)^{4}(1 +\alpha)^{4}$   &  $\frac{1382}{14175}
 (-1 +\alpha)^{4}(1 +\alpha)^{4}$  \\
    & 2 & $\frac{88}{567}(-1 +\alpha)^{3}(1 +\alpha)^{3}  (1+ 3 \alpha ^{2})$ &
 $\frac{848}{945} (-1 +\alpha)^{3}(1 +\alpha)^{3} (1 +  \alpha ^{2})$    \\
    & 3 & $\frac{16}{45}(-1 +\alpha)^{3}(1 +\alpha)^{3} (1+ 10 \alpha ^{2} +  5 \alpha ^{4})$  &
    $\frac{37}{45}(-1 +\alpha)^{2}(1 +\alpha)^{2} (3+ \alpha ^{2})(1+ 3\alpha ^{2})$
 \\
    & 4 & $\frac{1}{3}(-1 +\alpha)(1 +\alpha) (1 +21\alpha ^{2}+35  \alpha ^{4}+7 \alpha ^{6})$ &
    $\frac{8}{3}(-1 +\alpha)(1 +\alpha) (1 + \alpha ^{2})(1+ 6 \alpha ^{2}+  \alpha ^{4})$ \\
    & 5 & $\frac{1}{9} ( 1 + 36\alpha ^{2} + 126 \alpha ^{4} + 84 \alpha ^{6}+
 9 \alpha ^{8} )$   &  $\frac{1}{5} ( 5 + 10 \alpha ^{2} +  \alpha ^{4})(1 + 10 \alpha ^{2}+ 5 \alpha ^{4} )$  \\  
\hline 
\end{tabular}}%\vspace*{1.5mm}
\end{table}