ciegf={0, 1, n*a[2], (n*(3*(-1 + n)*a[2]^2 + 2*a[3]))/2, 
 (n*(3*(3 - 5*n + 2*n^2)*a[2]^3 + 10*(-1 + n)*a[2]*a[3] + 2*a[4]))/2, 
 (n*(15*(-8 + 18*n - 13*n^2 + 3*n^3)*a[2]^4 + 5*(37 - 63*n + 26*n^2)*a[2]^2*a[3] + 
    45*(-1 + n)*a[2]*a[4] + 6*(5*(-1 + n)*a[3]^2 + a[5])))/6, 
 (n*(45*(62 - 175*n + 178*n^2 - 77*n^3 + 12*n^4)*a[2]^5 + 
    30*(-184 + 427*n - 320*n^2 + 77*n^3)*a[2]^3*a[3] + 360*(4 - 7*n + 3*n^2)*a[2]^2*
     a[4] + 28*(-1 + n)*a[2]*(10*(-7 + 5*n)*a[3]^2 + 9*a[5]) + 
    12*(35*(-1 + n)*a[3]*a[4] + 2*a[6])))/24, 
 (n*(63*(-314 + 1075*n - 1405*n^2 + 875*n^3 - 261*n^4 + 30*n^5)*a[2]^6 + 
    42*(1144 - 3350*n + 3545*n^2 - 1600*n^3 + 261*n^4)*a[2]^4*a[3] + 
    420*(-31 + 75*n - 59*n^2 + 15*n^3)*a[2]^3*a[4] + 28*(-1 + n)*a[2]^2*
     (5*(193 - 262*n + 85*n^2)*a[3]^2 + 18*(-5 + 4*n)*a[5]) + 
    56*(-1 + n)*a[2]*(5*(-31 + 23*n)*a[3]*a[4] + 6*a[6]) + 
    4*(70*(7 - 12*n + 5*n^2)*a[3]^3 + 168*(-1 + n)*a[3]*a[5] + 
      3*(35*(-1 + n)*a[4]^2 + 2*a[7]))))/24, 
 (n*(63*(1298 - 5301*n + 8510*n^2 - 6900*n^3 + 3002*n^4 - 669*n^5 + 60*n^6)*a[2]^7 + 
    21*(-11282 + 40257*n - 54830*n^2 + 35625*n^3 - 11108*n^4 + 1338*n^5)*a[2]^5*a[3] + 
    105*(628 - 1935*n + 2162*n^2 - 1035*n^3 + 180*n^4)*a[2]^4*a[4] + 
    28*(-1 + n)*a[2]^3*(4*(-1652 + 3298*n - 2062*n^2 + 413*n^3)*a[3]^2 + 
      15*(32 - 49*n + 18*n^2)*a[5]) + 14*(-1 + n)*a[2]^2*
     (75*(68 - 97*n + 33*n^2)*a[3]*a[4] + 2*(-73 + 62*n)*a[6]) + 
    2*(-1 + n)*a[2]*(210*(78 - 107*n + 35*n^2)*a[3]^3 + 35*(-77 + 58*n)*a[4]^2 + 
      56*(-76 + 59*n)*a[3]*a[5] + 108*a[7]) + 
    4*(70*(26 - 45*n + 19*n^2)*a[3]^2*a[4] + 126*(-1 + n)*a[3]*a[6] + 
      3*(63*(-1 + n)*a[4]*a[5] + a[8]))))/12}


ciogf={0, 1, n*a[2], (n*(12*(-1 + n)*a[2]^2 + 12*a[3]))/12, 
 (n*(24*(3 - 5*n + 2*n^2)*a[2]^3 + 120*(-1 + n)*a[2]*a[3] + 48*a[4]))/48, 
 (n*(240*(-8 + 18*n - 13*n^2 + 3*n^3)*a[2]^4 + 120*(37 - 63*n + 26*n^2)*a[2]^2*a[3] + 
    2160*(-1 + n)*a[2]*a[4] + 6*(180*(-1 + n)*a[3]^2 + 120*a[5])))/720, 
 (n*(1440*(62 - 175*n + 178*n^2 - 77*n^3 + 12*n^4)*a[2]^5 + 
    1440*(-184 + 427*n - 320*n^2 + 77*n^3)*a[2]^3*a[3] + 
    34560*(4 - 7*n + 3*n^2)*a[2]^2*a[4] + 56*(-1 + n)*a[2]*
     (360*(-7 + 5*n)*a[3]^2 + 1080*a[5]) + 12*(5040*(-1 + n)*a[3]*a[4] + 1440*a[6])))/
  17280, (n*(4032*(-314 + 1075*n - 1405*n^2 + 875*n^3 - 261*n^4 + 30*n^5)*a[2]^6 + 
    4032*(1144 - 3350*n + 3545*n^2 - 1600*n^3 + 261*n^4)*a[2]^4*a[3] + 
    80640*(-31 + 75*n - 59*n^2 + 15*n^3)*a[2]^3*a[4] + 
    112*(-1 + n)*a[2]^2*(180*(193 - 262*n + 85*n^2)*a[3]^2 + 2160*(-5 + 4*n)*a[5]) + 
    112*(-1 + n)*a[2]*(720*(-31 + 23*n)*a[3]*a[4] + 4320*a[6]) + 
    4*(15120*(7 - 12*n + 5*n^2)*a[3]^3 + 120960*(-1 + n)*a[3]*a[5] + 
      3*(20160*(-1 + n)*a[4]^2 + 10080*a[7]))))/120960, 
 (n*(8064*(1298 - 5301*n + 8510*n^2 - 6900*n^3 + 3002*n^4 - 669*n^5 + 60*n^6)*a[2]^7 + 
    4032*(-11282 + 40257*n - 54830*n^2 + 35625*n^3 - 11108*n^4 + 1338*n^5)*a[2]^5*
     a[3] + 40320*(628 - 1935*n + 2162*n^2 - 1035*n^3 + 180*n^4)*a[2]^4*a[4] + 
    224*(-1 + n)*a[2]^3*(144*(-1652 + 3298*n - 2062*n^2 + 413*n^3)*a[3]^2 + 
      1800*(32 - 49*n + 18*n^2)*a[5]) + 56*(-1 + n)*a[2]^2*
     (10800*(68 - 97*n + 33*n^2)*a[3]*a[4] + 1440*(-73 + 62*n)*a[6]) + 
    4*(-1 + n)*a[2]*(45360*(78 - 107*n + 35*n^2)*a[3]^3 + 20160*(-77 + 58*n)*a[4]^2 + 
      40320*(-76 + 59*n)*a[3]*a[5] + 544320*a[7]) + 
    4*(60480*(26 - 45*n + 19*n^2)*a[3]^2*a[4] + 544320*(-1 + n)*a[3]*a[6] + 
      3*(181440*(-1 + n)*a[4]*a[5] + 40320*a[8]))))/483840}