s(3) in [[1.0512699547942366362607949299748872654642626060299875932522213000674665299888398475869344395050575258210301399230957031 +/- 9.86e-120], [1.0512699547942366362607949299748872654717857698752502333032212139056889023268793071502757996427135367412120103836059570 +/- 4.30e-119]]; grid starts at the lower end
building series at 221 grid points on [1.0512700, 8.00000] ...
  0/220
  40/220
  80/220
  120/220
  160/220
  200/220

    k     3^k T_k (upper)      vs CN=367.8435
   59         34.13749969      OK
   60         31.92944175      OK
   65         22.89700945      OK
   70         16.39083814      OK
   75         11.41683175      OK
   80         7.708219010      OK
   90         3.441739550      OK
  100         1.533695217      OK
  120        0.2976807887      OK
  150       0.02199293551      OK
  180      0.001462082531      OK
  200     0.0002254410762      OK
  (all 142 values of k in [59, 200] evaluated; only a sample printed)

k-tail, Cauchy at R = 3.15000:
  int M_R e^{aR} ds + tail = 175345.2269
  (3/R)^201 = 5.507e-05,  so 3^k T_k <= 9.657057900 for every k > 200

worst over the whole head k in [59, 200]: 34.13749969 at k = 59
bound for k > 200:              9.657057900

CERTIFIED: 3^k T_k <= CN = 367.8435 for all k >= 59