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A173988 Triangle T(n,k) = 2^(k-1)*n*binomial(n-k,2*k-2)/(n-3*k+3) if k<n/3+1, else T(n,k)=1. 0

%I

%S 1,1,1,8,1,15,1,24,1,1,35,28,1,48,80,1,1,63,180,1,1,80,350,80,1,1,99,

%T 616,308,1,1,120,1008,896,1,1,1,143,1560,2184,208,1,1,168,2310,4704,

%U 1008,1,1,1,195,3300,9240,3600,1,1,1,224,4576,16896,10560,512,1,1,1,255,6188,29172

%N Triangle T(n,k) = 2^(k-1)*n*binomial(n-k,2*k-2)/(n-3*k+3) if k<n/3+1, else T(n,k)=1.

%C Row sums are 1, 1, 9, 16, 26, 64, 130, 245, 512, 1025, 2027,...

%e The triangle starts in row n=2 with columns 1<= k <= n/2 as:

%e 1;

%e 1;

%e 1, 8;

%e 1, 15;

%e 1, 24, 1;

%e 1, 35, 28;

%e 1, 48, 80, 1;

%e 1, 63, 180, 1;

%e 1, 80, 350, 80, 1;

%e 1, 99, 616, 308, 1;

%e 1, 120, 1008, 896, 1, 1;

%t g[n_, k_] = If[(n - 3*k + 3) > 0, 2^k*n*Binomial[n - k, 2*k - 2]/(n - 3*k + 3), 2]/2;

%t Table[Table[g[n, k], {k, 1, Floor[n/2]}], {n, 2, 12}];

%t Flatten[%]

%K nonn,easy,tabf

%O 2,4

%A _Roger L. Bagula_, Mar 04 2010

%E Tabl replaced by tabf, replaced Mma notation, extended beyond n=12, removed broken link w/o author or title - The Assoc. Eds. of the OEIS - Nov 02 2010

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Last modified January 19 08:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)