%N Numerators for the "Minimum-Redundancy Code" card problem.
%C Given a deck of cards consisting of one 1, two 2's, three 3's, ..., n n's, what's the best average number of yes-or-no questions needed to ask to determine a randomly drawn card? The answer is the above sequence divided by the number of cards (A000217).
%C The problem can be solved using Huffman codes.
%C This problem was popularized in Martin Gardner's Scientific American "Mathematical Games" column, and was included in his book "My Best Mathematical and Logic Puzzles".
%D Gardner, M. (1995). My best mathematical and logic puzzles. New York: Dover Publications Inc, p29, puzzle #52 "Playing Twenty Questions when Probability Values Are Known"
%H D. A. Huffman, <a href="https://www.ic.tu-berlin.de/fileadmin/fg121/Source-Coding_WS12/selected-readings/10_04051119.pdf">A Method for the Construction of Minimum-Redundancy Codes</a>, in Proceedings of the IRE, vol. 40, no. 9, pp. 1098-1101, Sept. 1952.
%e For n=2, there are 3 cards, so a(2)/3 = 3/3 = 1 question is needed on average.
%e For n=3, there are 6 cards, so a(3)/6 = 9/6 = 1.5 questions are needed on average.
%Y Cf. A286496.
%A _Danny Pflughoeft_, Nov 10 2019