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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
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
2,2
COMMENTS
This triangle was mentioned in A143420 with the wrong A-number A143419.
EXAMPLE
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;
MAPLE
seq(print(n, seq((binomial(n, k)^3 - binomial(n, k))/6, k=1..n-1)), n=2..10);
CROSSREFS
Sequence in context: A145598 A320392 A117881 * A342989 A377149 A161719
KEYWORD
nonn,easy,tabl
AUTHOR
Georg Fischer, May 23 2024
STATUS
approved