cp's OEIS Frontend

A356013 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).

%I A356013 #12 Jul 23 2022 09:54:12
%S A356013 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 A356013 42,7,1,5040,5040,3360,840,336,56,8,1,40320,45360,20160,7560,3024,504,
%U A356013 72,9,1,362880,362880,201600,75600,15120,5040,720,90,10,1
%N A356013 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).
%F A356013 E.g.f. of column k: -(1 - x^k) * log(1 - x^k)/(k! * (1 - x)).
%e A356013 Triangle begins:
%e A356013       1;
%e A356013       1,     1;
%e A356013       2,     3,     1;
%e A356013       6,     6,     4,    1;
%e A356013      24,    30,    20,    5,    1;
%e A356013     120,   120,    60,   30,    6,   1;
%e A356013     720,   840,   420,  210,   42,   7,  1;
%e A356013    5040,  5040,  3360,  840,  336,  56,  8, 1;
%e A356013   40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1;
%e A356013   ...
%o A356013 (PARI) T(n, k) = n!/(k!*(n\k));
%Y A356013 Row sums gives A356011.
%Y A356013 Column k=1..3 give A000142(n-1), |A265376(n)|, A356012.
%Y A356013 Cf. A355996.
%K A356013 nonn,tabl
%O A356013 1,4
%A A356013 _Seiichi Manyama_, Jul 23 2022