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A344118 Triangle of numbers T(n,k) = floor((A089072(n,k)-A019538(n,k))/A019538(n,k)) read by rows, n>=1, 1<=k<=n.

%I A344118 #11 Mar 22 2025 02:13:43
%S A344118 0,0,1,0,0,3,0,0,1,9,0,0,0,3,25,0,0,0,1,7,63,0,0,0,0,3,17,162,0,0,0,0,
%T A344118 2,7,39,415,0,0,0,0,1,4,16,91,1066,0,0,0,0,0,2,8,34,212,2754,0,0,0,0,
%U A344118 0,1,5,16,73,500,7146,0,0,0,0,0,1,3,9,33,160,1190,18612,0
%N A344118 Triangle of numbers T(n,k) = floor((A089072(n,k)-A019538(n,k))/A019538(n,k)) read by rows, n>=1, 1<=k<=n.
%F A344118 T(n, k) = floor((k^n - k!*Stirling2(n, k))/(k!*Stirling2(n, k))).
%e A344118 T(3, 3) = floor((27-6)/6) = 3.
%e A344118 Triangle begins:
%e A344118   0
%e A344118   0    1
%e A344118   0    0    3
%e A344118   0    0    1    9
%e A344118   0    0    0    3    25
%e A344118   0    0    0    1    7    63
%e A344118   0    0    0    0    3    17    162
%t A344118 Floor[Table[(k^n - k!*StirlingS2[n, k])/(k!*StirlingS2[n, k]), {n, 15}, {k, n}]] // Flatten
%Y A344118 Cf. A008277, A008292, A028246, A089072, A019538.
%K A344118 easy,nonn,tabl
%O A344118 1,6
%A A344118 _Mohammad K. Azarian_, Jul 28 2021