A111126 Triangle read by rows: T(k,s) = binomial(k+s,2s+1)*(2k-1)*(2k+1)/(2s+3), k >= 1, 0 <= s <= k-1.

1, 10, 3, 35, 28, 5, 84, 126, 54, 7, 165, 396, 297, 88, 9, 286, 1001, 1144, 572, 130, 11, 455, 2184, 3510, 2600, 975, 180, 13, 680, 4284, 9180, 9350, 5100, 1530, 238, 15, 969, 7752, 21318, 28424, 20995, 9044, 2261, 304, 17, 1330, 13167, 45144, 76076, 72618

Offset: 1

Author

N. J. A. Sloane, Oct 16 2005

Keywords

• nonn
• easy
• tabl

Examples

			Triangle starts:
1;
10,3;
35,28,5;
84,126,54,7;
165,396,297,88,9;
		

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 A111127. Cf. A111125, A082985, A100218, A098599.

Programs

Maple

T:=(k,s)->binomial(k+s,2*s+1)*(2*k-1)*(2*k+1)/(2*s+3): for k from 1 to 10 do seq(T(k,s),s=0..k-1) od; # yields sequence in triangular form; Emeric Deutsch, Feb 01 2006

Extensions

More terms from Emeric Deutsch, Feb 01 2006