|
%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
|
