A215564 - OEIS

%I #6 Oct 07 2015 21:28:39

%S 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,

%T 1430,1,9,51,204,612,1428,2652,3978,4862,1

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

%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,/* p=3 */

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

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

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

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

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

%e 1,9,51,204,612,1428,2652,3978,4862,/* p=19 */

%e etc.

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

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

%K nonn

%O 1,4

%A _M. F. Hasler_, Aug 16 2012