%I #7 Dec 21 2023 15:41:27

%S 1,1,2,8,388,2495,13652575732976,1580140554389506598141638,

%T 2303282945504494379369753334706333784257298061180917309,

%U 1116351824215919296474220471583292515147278170740521646743561595082143234790184233409933250330039986837258312677349601942095851

%N Numerator of the greatest probability that a particular free polyomino with n cells appears as the image of a simple random walk on the square lattice.

%C a(n) is the numerator of the maximum of A367994/A367995 over the n-th row. See A367994 for details.

%H Pontus von Brömssen, <a href="/A367998/b367998.txt">Table of n, a(n) for n = 1..13</a>.

%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

%e For 1 <= n <= 13, the following are all polyominoes that have the maximum probabilities for their respective sizes. Except for n = 7, there is just one such polyomino.

%e _ _ _ _

%e _ _ | | | |_ | |

%e _ | | | |_ | |_ | | | |

%e |_| |_| |_ _| |_ _| |_ _| |_ _|

%e _ _ _

%e _ _ | |_ _ _ _| |

%e | | | | | |_ | _|

%e | |_ | | | | | |

%e |_ _ _| |_ _| |_ _ _| |_ _|

%e _ _ _ _ _ _ _ _ _

%e | | | |_ _| |_ _| |

%e | |_ | | | | | _|

%e | | | | | _ _| | |

%e |_ _ _| |_ _ _| |_ _| |_ _ _|

%Y Cf. A367673, A367762, A367994, A367995, A367996, A367999 (denominators), A368004.

%K nonn,frac

%O 1,3

%A _Pontus von Brömssen_, Dec 08 2023