A092113 Triangle read by rows: T(n,k) is the number of stacks of n pancakes requiring k = 0, ..., A058986(n) flips to sort.

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, 30, 149, 543, 1357, 1903, 1016, 35, 1, 7, 42, 251, 1191, 4281, 10561, 15011, 8520, 455, 1, 8, 56, 391, 2278, 10666, 38015, 93585, 132697, 79379, 5804, 1, 9, 72, 575

Offset: 1

Author

Eric W. Weisstein, Feb 21 2004

Keywords

• nonn
• tabf

Comments

Last term of row k is A067607(k).

Row n has length A058986(n) + 1. - Martin Renner, Jul 23 2017

Examples

			Triangle begins:
  1;
  1,  1;
  1,  2,  2,  1;
  1,  3,  6, 11,  3;
  1,  4, 12, 35, 48, 20;
  ...
From _Jon E. Schoenfield_, Dec 16 2021: (Start)
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,
T(3,0)=1 permutation (namely, {1,2,3}) requires no prefix reversals (because it is already sorted);
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};
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
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};
thus, the terms in row n=3 are 1, 2, 2, 1. (End)
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..97 (terms 1..68 from Martin Renner)

Crossrefs

Cf. A058986, A067607.