Dear Funsters Imagine n pennies in a frying pan. They are all flipped randomly at once and those landing heads are removed and placed heads up on a flat surface. The process is repeated with the remaining pennies until all coins show heads. What is the expected number of flips, f(n), for n coins? f(1) = 2, f(2) = 8/3, f(3) = 66/3/7, f(4) = 1104/3/7/15, f(5) = 37050/3/7/15/31 etc. The numerators follow the sequence 2, 8, 66, 1104, 37050, 2482200, 31336530, 88081529760, 46640940221610.... 1. I don't find this sequence in the OEIS. Should it be there or is there a related sequence that is there? 2 f(64) = 7.34399... f(128) = 8.33837... f(256) = 9.33556... f(512) = 10.33415... f(1024) = 11.33345... f(2048) = 12.33309... f(4096) = 13.33292... f(8192) = 14.33283... f(16384) = 15.3327... Perhaps someone can verify these results and determine the limit of e(k) as k approaches infinity for f(2^k) = k+1+e(k). Any help is appreciated. Dick Hess