A111126 - OEIS

%I #10 Mar 08 2016 02:50:18

%S 1,10,3,35,28,5,84,126,54,7,165,396,297,88,9,286,1001,1144,572,130,11,

%T 455,2184,3510,2600,975,180,13,680,4284,9180,9350,5100,1530,238,15,

%U 969,7752,21318,28424,20995,9044,2261,304,17,1330,13167,45144,76076,72618

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

%H K. Dilcher and K. B. Stolarsky, <a href="http://www.maa.org/programs/maa-awards/writing-awards/a-pascal-type-triangle-characterizing-twin-primes">A Pascal-type triangle characterizing twin primes</a>, Amer. Math. Monthly, 112 (2005), 673-681.

%e Triangle starts:

%e 1;

%e 10,3;

%e 35,28,5;

%e 84,126,54,7;

%e 165,396,297,88,9;

%p 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

%Y Mirror image of A111127. Cf. A111125, A082985, A100218, A098599.

%K nonn,easy,tabl

%O 1,2

%A _N. J. A. Sloane_, Oct 16 2005

%E More terms from _Emeric Deutsch_, Feb 01 2006