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%I #25 Dec 24 2023 01:10:19
%S 1,1,1,1,2,2,1,1,3,6,11,3,1,4,12,35,48,20,1,5,20,79,199,281,133,2,1,6,
%T 30,149,543,1357,1903,1016,35,1,7,42,251,1191,4281,10561,15011,8520,
%U 455,1,8,56,391,2278,10666,38015,93585,132697,79379,5804,1,9,72,575
%N Triangle read by rows: T(n,k) is the number of stacks of n pancakes requiring k = 0, ..., A058986(n) flips to sort.
%C Last term of row k is A067607(k).
%C Row n has length A058986(n) + 1. - _Martin Renner_, Jul 23 2017
%H Sean A. Irvine, <a href="/A092113/b092113.txt">Table of n, a(n) for n = 1..97</a> (terms 1..68 from Martin Renner)
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 2, 2, 1;
%e 1, 3, 6, 11, 3;
%e 1, 4, 12, 35, 48, 20;
%e ...
%e From _Jon E. Schoenfield_, Dec 16 2021: (Start)
%e For n=3, the 3! = 6 permutations are {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, and {3,2,1}. Of these,
%e T(3,0)=1 permutation (namely, {1,2,3}) requires no prefix reversals (because it is already sorted);
%e T(3,1)=2 permutations (namely, {2,1,3} and {3,2,1}) require one prefix reversal, e.g., {2,1,3} -> {1,2,3};
%e T(3,2)=2 permutations (namely, {2,3,1} and {3,1,2}) require two prefix reversals, e.g., {2,3,1} -> {3,2,1} -> {1,2,3}; and
%e T(3,3)=1 permutation (namely, {1,3,2}) requires 3 prefix reversals: {1,3,2} -> {3,1,2} -> {2,1,3} -> {1,2,3};
%e thus, the terms in row n=3 are 1, 2, 2, 1. (End)
%Y Cf. A058986, A067607.
%K nonn,tabf
%O 1,5
%A _Eric W. Weisstein_, Feb 21 2004
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