%I #5 Mar 17 2014 01:36:33

%S 1,1,1,1,3,1,1,5,6,1,1,7,13,10,1,1,9,22,25,15,1,1,11,33,46,41,21,1,1,

%T 13,46,73,79,61,28,1,1,15,61,106,129,121,85,36,1,1,17,78,145,191,201,

%U 172,113,45,1,1,19,97,190,265,301,289,232,145,55,1,1,21

%N Square array, read by antidiagonals: column k has g.f. (1+(k-1)*x)^2/(1-x)^3.

%F T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k).

%F T(n,k) = 3*T(n,k-1) - 3*T(n,k-2) + T(n,k-3).

%F T(n,k) = (T(n,k-1) + T(n,k+1))/2 - A161680(n).

%F T(n,k) = (T(n-1,k) + T(n+1,k) - A000290(n))/2.

%e Square array begins:

%e n\k : 0......1......2......3......4......5......6......7......8......9

%e ======================================================================

%e .0|| 1......1......1......1......1......1......1......1......1......1

%e .1|| 1......3......5......7......9.....11.....13.....15.....17.....19

%e .2|| 1......6.....13.....22.....33.....46.....61.....78.....97....118

%e .3|| 1.....10.....25.....46.....73....106....145....190....241....298

%e .4|| 1.....15.....41.....79....129....191....265....351....449....559

%e .5|| 1.....21.....61....121....201....301....421....561....721....901

%e .6|| 1.....28.....85....172....289....436....613....820...1057...1324

%e .7|| 1.....36....113....232....393....596....841...1128...1457...1828

%e .8|| 1.....45....145....301....513....781...1105...1485...1921...2413

%e .9|| 1.....55....181....379....649....991...1405...1891...2449...3079

%e 10|| 1.....66....221....466....801...1226...1741...2346...3041...3826

%e 11|| 1.....78....265....562....969...1486...2113...2850...3697...4654

%Y Cf. Columns: A000012, A000217, A001844, A038764, A081585, A081587, A081589, A081591, A081593.

%Y Cf. Rows: A000012, A005408, A028872, A100536, A239325, A069133.

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Mar 16 2014