Table 3 The polinomial coefficients

0

3 + 10π

1

3 + 10π + 12π²

2

$\frac{3}{2}+5\pi +38{\pi }^2$

3

$\frac{1}{2}+\frac{5\pi }{3}+\frac{38{\pi }^2}{3}+20{\pi }^3$

4

$\frac{1}{8}+\frac{5\pi }{12}+\frac{19{\pi }^2}{6}+37{\pi }^3$

5

$\frac{1}{40}+\frac{\pi }{12}+\frac{19{\pi }^2}{30}+\frac{37{\pi }^3}{5}+14{\pi }^4$

6

$\frac{1}{240}+\frac{\pi }{72}+\frac{19{\pi }^2}{180}+\frac{37{\pi }^3}{30}+\frac{97{\pi }^4}{5}$

7

$\frac{1}{1680}+\frac{\pi }{504}+\frac{19{\pi }^2}{1260}+\frac{37{\pi }^3}{210}+\frac{97{\pi }^4}{35}+6{\pi }^5$

8

$\frac{1}{13440}+\frac{\pi }{4032}+\frac{19{\pi }^2}{10080}+\frac{37{\pi }^3}{1680}+\frac{97{\pi }^4}{280}+\frac{575{\pi }^5}{84}$

9

$\frac{1}{120960}+\frac{\pi }{36288}+\frac{19{\pi }^2}{90720}+\frac{37{\pi }^3}{15120}+\frac{97{\pi }^4}{2520}+\frac{575{\pi }^5}{756}+\frac{11{\pi }^6}{6}$

10

$\frac{1}{1209600}+\frac{\pi }{362880}+\frac{19{\pi }^2}{907200}+\frac{37{\pi }^3}{151200}+\frac{97{\pi }^4}{25200}+\frac{115{\pi }^5}{1512}+\frac{2279{\pi }^6}{1260}$

11

$\frac{1}{\text{13305600}}+\frac{\pi }{\text{3991680}}+\frac{19{\pi }^2}{\text{9979200}}+\frac{\text{37}{\pi }^{\text{3}}}{\text{1663200}}+\frac{\text{97}{\pi }^{\text{4}}}{\text{277200}}+\frac{\text{1}15{\pi }^5}{\text{16632}}+\frac{2279{\pi }^6}{13860}+\frac{13{\pi }^7}{30}$

12

$\frac{1}{\text{159667200}}+\frac{\pi }{\text{47900160}}+\frac{19{\pi }^2}{\text{119750400}}+\frac{\text{37}{\pi }^{\text{3}}}{\text{19958400}}+\frac{\text{97}{\pi }^{\text{4}}}{\text{3326400}}+\frac{\text{1}15{\pi }^5}{\text{199584}}+\frac{2279{\pi }^6}{166320}+\frac{905{\pi }^7}{2376}$