A108359 - OEIS

%I #6 Dec 05 2016 02:40:50

%S 1,1,1,1,3,1,1,5,5,1,1,7,14,7,1,1,9,28,28,9,1,1,11,47,76,47,11,1,1,13,

%T 71,163,163,71,13,1,1,15,100,301,433,301,100,15,1,1,17,134,502,961,

%U 961,502,134,17,1,1,19,173,778,1879,2515,1879,778,173,19,1,1,21,217,1141

%N A symmetric number triangle based on floor((n+2)/2).

%C Row sums are A108360. Diagonal sums are A108361.

%F Number triangle T(n,k) = Sum_{j=0..n-k} binomial(k,j)*binomial(n-j,k)*floor((j+2)/2). As a square array read by antidiagonals, T(n,k) = Sum_{j=0..n} binomial(k,j)*binomial(n+k-j,k)*floor((j+2)/2).

%e Rows begin

%e   1;

%e   1,  1;

%e   1,  3,  1;

%e   1,  5,  5,  1;

%e   1,  7, 14,  7,  1;

%e   1,  9, 28, 28,  9,  1;

%e   1, 11, 47, 76, 47, 11,  1;

%e As a square array read by antidiagonals, rows start

%e   1,  1,   1,   1,    1,    1, ...

%e   1,  3,   5,   7,    9,   11, ...

%e   1,  5,  14,  28,   47,   71, ...

%e   1,  7,  28,  76,  163,  301, ...

%e   1,  9,  47, 163,  433,  961, ...

%e   1, 11,  71, 301,  961, 2515, ...

%e   1, 13, 100, 502, 1879, 5695, ...

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, May 31 2005