A111127 Triangle read by rows: T(k,s)=(2k-1)(2k+1)binomial(2k-s-1,2k-2s-1)/(2k-2s+1); k>=1, 0<=s<=k-1.
1, 3, 10, 5, 28, 35, 7, 54, 126, 84, 9, 88, 297, 396, 165, 11, 130, 572, 1144, 1001, 286, 13, 180, 975, 2600, 3510, 2184, 455, 15, 238, 1530, 5100, 9350, 9180, 4284, 680, 17, 304, 2261, 9044, 20995, 28424, 21318, 7752, 969, 19, 378, 3192, 14896, 41895, 72618
Offset: 1
Examples
Triangle starts: 1; 3,10; 5,28,35; 7,54,126,84; 9,88,297,396,165;
Links
- K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing twin primes, Amer. Math. Monthly, 112 (2005), 673-681.
Crossrefs
Mirror image of A111126.
Programs
-
Maple
T:=(k,s)->binomial(2*k-s-1,2*k-2*s-1)*(2*k-1)*(2*k+1)/(2*k-2*s+1): for k from 1 to 10 do seq(T(k,s),s=0..k-1) od; # yields sequence in triangular form; Emeric Deutsch, Feb 02 2006
Extensions
More terms from Emeric Deutsch, Feb 02 2006