A373101 Triangle read by rows, T(n,k) = (binomial(n,k)^3 - binomial(n,k))/6 for k=1..n-1 and n >= 2.

1, 4, 4, 10, 35, 10, 20, 165, 165, 20, 35, 560, 1330, 560, 35, 56, 1540, 7140, 7140, 1540, 56, 84, 3654, 29260, 57155, 29260, 3654, 84, 120, 7770, 98770, 333375, 333375, 98770, 7770, 120, 165, 15180, 287980, 1543465, 2667126, 1543465, 287980, 15180, 165

Offset: 2

Author

Georg Fischer, May 23 2024

Keywords

• nonn
• easy
• tabl

Comments

This triangle was mentioned in A143420 with the wrong A-number A143419.

Examples

			T(n,k) for n=2..7:
   1;
   4,    4;
  10,   35,   10;
  20,  165,  165,   20;
  35,  560, 1330,  560,   35;
  56, 1540, 7140, 7140, 1540, 56;
		

Crossrefs

Cf. A143418, A143420.

Programs

Maple

seq(print(n,seq((binomial(n,k)^3 - binomial(n,k))/6,k=1..n-1)),n=2..10);