A215563 - OEIS

%I #4 Aug 16 2012 09:43:57

%S 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,

%T 132,99,55,22,6,1,1,8,40,140,364,728,1144,1430,1430,1144,728,364,140,

%U 40,8,1,1,9,51,204,612,1428,2652,3978,4862,4862,3978,2652,1428,612,204,51,9,1

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

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

%e Formatted as an irregular triangular table, the sequence reads:

%e 1,/* p=2 */

%e 1,1,/* p=3 */

%e 1,2,2,1,/* p=5 */

%e 1,3,5,5,3,1,/* p=7 */

%e 1,5,15,30,42,42,30,15,5,1,/* p=11 */

%e 1,6,22,55,99,132,132,99,55,22,6,1,/* p=13 */

%e 1,8,40,140,364,728,1144,1430,1430,1144,728,364,140,40,8,1,/* p=17 */

%e etc.

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

%K nonn

%O 1,5

%A _M. F. Hasler_, Aug 16 2012