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Product matrix [C(k,n-k)]*A001263.
0

%I #2 Mar 30 2012 18:59:25

%S 1,1,1,2,4,1,3,12,8,1,5,31,39,13,1,8,73,148,93,19,1,13,162,481,486,

%T 186,26,1,21,344,1406,2080,1274,332,34,1,34,707,3803,7741,6920,2873,

%U 547,43,1

%N Product matrix [C(k,n-k)]*A001263.

%C First column is A000045. Row sums are A052705(n+2).

%F Number triangle T(n,k)=sum{j=0..n, C(j,n-j)*C(j+1,k)*C(j+1,k+1)/(j+1)}.

%e Triangle begins

%e 1,

%e 1, 1,

%e 2, 4, 1,

%e 3, 12, 8, 1,

%e 5, 31, 39, 13, 1,

%e 8, 73, 148, 93, 19, 1,

%e 13, 162, 481, 486, 186, 26, 1,

%e 21, 344, 1406, 2080, 1274, 332, 34, 1

%K easy,nonn,tabl

%O 0,4

%A _Paul Barry_, Jun 30 2009