A120695 - OEIS

%I #16 Mar 28 2018 05:13:29

%S 0,1,3,5,9,15,11,17,23,33,57,39,63,87,35,59,83,41,65,89,47,71,95,119,

%T 153,273,177,297,417,159,279,399,183,303,423,207,327,447,567,155,275,

%U 395,179,299,419,203,323,443,563,161,281,401,185,305,425,209,329,449

%N Set partitions reversed interpreted as factorial base numbers.

%H Alois P. Heinz, <a href="/A120695/b120695.txt">Rows n = 0..9, flattened</a>

%e The third set partition is {1,2}, 21 in base factorial is 5, so a(3) = 5.

%e Triangle begins:

%e    0;

%e    1;

%e    3,  5;

%e    9, 15, 11, 17, 23;

%e   33, 57, 39, 63, 87, 35, 59, 83, 41, 65, 89, 47, 71, 95, 119;

%p b:= proc(n, m, t) option remember; `if`(n=0, [0], [seq(map(

%p        x-> x+j*t!, b(n-1, max(m, j), t+1))[], j=1..m+1)])

%p     end:

%p T:= n-> b(n, 0, 1)[]:

%p seq(T(n), n=0..5);  # _Alois P. Heinz_, Apr 04 2016

%Y Cf. A000110 (row lengths), A120698, A120696 (sorted), A120697, A071155.

%Y Column k=0 gives A007489.

%K base,nonn,look,tabf

%O 0,3

%A _Franklin T. Adams-Watters_, Jun 28 2006