A215563 C(p,k)/p for primes p and k=1,...,p-1.

1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 5, 3, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1, 8, 40, 140, 364, 728, 1144, 1430, 1430, 1144, 728, 364, 140, 40, 8, 1, 1, 9, 51, 204, 612, 1428, 2652, 3978, 4862, 4862, 3978, 2652, 1428, 612, 204, 51, 9, 1

Offset

1,5

Comments

Motivated by the fact that any prime p divides the binomial coefficients C(p,k)=p!/k!(p-k)! for k=1,...,p-1.

Links

Table of n, a(n) for n=1..69.

Example

Formatted as an irregular triangular table, the sequence reads:
1,/* p=2 */
1,1,/* p=3 */
1,2,2,1,/* p=5 */
1,3,5,5,3,1,/* p=7 */
1,5,15,30,42,42,30,15,5,1,/* p=11 */
1,6,22,55,99,132,132,99,55,22,6,1,/* p=13 */
1,8,40,140,364,728,1144,1430,1430,1144,728,364,140,40,8,1,/* p=17 */
etc.

Prog

(PARI) forprime(p=1, 19, for(k=1, p-1, print1(binomial(p, k)/p", ")); print("/* p="p" */"))

Crossrefs

Sequence in context: A336706 A344567 A076037 * A076263 A272689 A274887

Adjacent sequences: A215560 A215561 A215562 * A215564 A215565 A215566

Keyword

nonn

Author

M. F. Hasler, Aug 16 2012

Status

approved