STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A215563
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing all changes.
STATUS
editing
proposed
NAME
allocated for M. F. Hasler
C(p,k)/p for primes p and k=1,...,p-1.
DATA
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.
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" */"))
KEYWORD
allocated
nonn
AUTHOR
M. F. Hasler, Aug 16 2012
STATUS
approved
editing
NAME
allocated for M. F. Hasler
KEYWORD
allocated
STATUS
approved