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

Author

N. J. A. Sloane, Oct 16 2005

Keywords

• nonn
• easy
• tabl

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