A215564 C(p,k)/p for primes p and 0 < k <= p/2.

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

Offset

1,4

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..36.

Example

Formatted as an irregular triangular table, the sequence reads:
1,/* p=2 */
1,/* p=3 */
1,2,/* p=5 */
1,3,5,/* p=7 */
1,5,15,30,42,/* p=11 */
1,6,22,55,99,132,/* p=13 */
1,8,40,140,364,728,1144,1430,/* p=17 */
1,9,51,204,612,1428,2652,3978,4862,/* p=19 */
etc.

Prog

(PARI) forprime(p=1, 19, for(k=1, p\2, print1(binomial(p, k)/p", ")); print("/* p="p" */"))

Crossrefs

Cf. A215563 for the "complete" triangle including the symmetric 2nd half.

Sequence in context: A286942 A125076 A220562 * A189449 A239286 A109533

Adjacent sequences: A215561 A215562 A215563 * A215565 A215566 A215567

Keyword

nonn

Author

M. F. Hasler, Aug 16 2012

Status

approved