A356013 - OEIS

%I #12 Jul 23 2022 09:54:12

%S 1,1,1,2,3,1,6,6,4,1,24,30,20,5,1,120,120,60,30,6,1,720,840,420,210,

%T 42,7,1,5040,5040,3360,840,336,56,8,1,40320,45360,20160,7560,3024,504,

%U 72,9,1,362880,362880,201600,75600,15120,5040,720,90,10,1

%N Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).

%F E.g.f. of column k: -(1 - x^k) * log(1 - x^k)/(k! * (1 - x)).

%e Triangle begins:

%e       1;

%e       1,     1;

%e       2,     3,     1;

%e       6,     6,     4,    1;

%e      24,    30,    20,    5,    1;

%e     120,   120,    60,   30,    6,   1;

%e     720,   840,   420,  210,   42,   7,  1;

%e    5040,  5040,  3360,  840,  336,  56,  8, 1;

%e   40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1;

%e   ...

%o (PARI) T(n, k) = n!/(k!*(n\k));

%Y Row sums gives A356011.

%Y Column k=1..3 give A000142(n-1), |A265376(n)|, A356012.

%Y Cf. A355996.

%K nonn,tabl

%O 1,4

%A _Seiichi Manyama_, Jul 23 2022