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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

%I #9 Mar 07 2016 21:43:57

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

%T 13,180,975,2600,3510,2184,455,15,238,1530,5100,9350,9180,4284,680,17,

%U 304,2261,9044,20995,28424,21318,7752,969,19,378,3192,14896,41895,72618

%N 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.

%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 3,10;

%e 5,28,35;

%e 7,54,126,84;

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

%p 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

%Y Mirror image of A111126.

%K nonn,easy,tabl

%O 1,2

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

%E More terms from _Emeric Deutsch_, Feb 02 2006

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)