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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.

%I A111126 #10 Mar 08 2016 02:50:18
%S A111126 1,10,3,35,28,5,84,126,54,7,165,396,297,88,9,286,1001,1144,572,130,11,
%T A111126 455,2184,3510,2600,975,180,13,680,4284,9180,9350,5100,1530,238,15,
%U A111126 969,7752,21318,28424,20995,9044,2261,304,17,1330,13167,45144,76076,72618
%N 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.
%H A111126 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 A111126 Triangle starts:
%e A111126 1;
%e A111126 10,3;
%e A111126 35,28,5;
%e A111126 84,126,54,7;
%e A111126 165,396,297,88,9;
%p A111126 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 A111126 Mirror image of A111127. Cf. A111125, A082985, A100218, A098599.
%K A111126 nonn,easy,tabl
%O A111126 1,2
%A A111126 _N. J. A. Sloane_, Oct 16 2005
%E A111126 More terms from _Emeric Deutsch_, Feb 01 2006