  We devise a three-parameter random search strategy to obtain accurate
estimates of the large-coupling amplitude and exponent of an observable from
its divergent Taylor expansion, known to some desired order. The endeavor
exploits the power of fractional calculus, aided by an auxiliary series and
subsequent construction of Pad\'e approximants. Pilot calculations on the
ground-state energy perturbation series of the octic anharmonic oscillator
reveal the spectacular performance.
