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.

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, 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, 0, 1, 5, 16, 73, 500, 7146, 0, 0, 0, 0, 0, 1, 3, 9, 33, 160, 1190, 18612, 0

Offset: 1

Author

Mohammad K. Azarian, Jul 28 2021

Keywords

• easy
• nonn
• tabl

Examples

			T(3, 3) = floor((27-6)/6) = 3.
Triangle begins:
  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
		

Crossrefs

Cf. A008277, A008292, A028246, A089072, A019538.

Programs

Mathematica

Floor[Table[(k^n - k!*StirlingS2[n, k])/(k!*StirlingS2[n, k]), {n, 15}, {k, n}]] // Flatten

Formula

T(n, k) = floor((k^n - k!*Stirling2(n, k))/(k!*Stirling2(n, k))).