This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350428 #8 Jun 02 2025 15:24:58 %S A350428 1,9,78,657,5448,49869,520416,5901138,70092000,902850273,12416814432, %T A350428 183763314090,2854581512832 %N A350428 2*a(n)/n! is the average number of key comparisons required to sort n records with distinct keys using heapsort (Algorithm H in Don Knuth's TAOCP Vol. 3). %C A350428 There are two places in the algorithm where the keys are compared. The first is in step H4 [Find larger child.] and the second in step H6 [Larger than K?]. The sequence is the sum, divided by 2, of the counts of these comparisons, taken over all n! possible orders of the records. %D A350428 D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 3, Sorting and Searching. Chapter 5.2.3 Sorting by Selection, Page 145. Addison-Wesley, Reading, MA, 1998. %Y A350428 Cf. A350426, A350427. %Y A350428 A350569 contains a table with the maximum and average number of comparisons for the original algorithm and for its modified version. %K A350428 nonn,more %O A350428 2,2 %A A350428 _Hugo Pfoertner_, Jan 05 2022