A144955 - OEIS

%I #2 Mar 30 2012 17:25:33

%S 1,2,0,3,1,0,4,4,1,0,5,10,6,1,0,6,20,21,8,1,0,7,35,56,36,10,1,0,8,56,

%T 126,120,55,12,1,9,84,252,330,220,78,14,1,10,120,462,792,715,364,105,

%U 16,1,11,165,792,1716,2002,1365,560,136,18,1

%N Binomial transform of a modified version of A026729

%C Row sums = A055588: (1, 2, 4, 9, 22, 56, 145,...).

%F Triangle A026729 is shifted one place down, with a (1, 1, 0, 0, 0...) in the first column; getting:

%F 1;

%F 1, 0;

%F 0, 1, 0;

%F 0, 1, 1, 0;

%F 0, 0, 2, 1, 0;

%F 0, 0, 1, 3, 1, 0;

%F ...

%F A144955 = A007318 * the modified triangle.

%e First few rows of the triangle =

%e 1;

%e 2, 0;

%e 3, 1, 0;

%e 4, 4, 1, 0;

%e 5, 10, 6, 1, 0;

%e 6, 20, 21, 8, 1, 0;

%e 7, 35, 56, 36, 10, 1, 0;

%e 8, 56, 126, 120, 55, 12, 1, 0;

%e ...

%Y A026729, Cf. A055588

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Sep 27 2008