A124376 - OEIS

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

%S 1,1,1,1,4,1,1,7,7,1,1,10,19,10,1,1,13,37,37,13,1,1,16,61,92,61,16,1,

%T 1,19,91,185,185,91,19,1,1,22,127,326,440,326,127,22,1,1,25,169,525,

%U 896,896,525,169,25,1,1,28,217,792

%N Number triangle with column k generated by x^k*(1+2kx+C(k,2)*x^2)/(1-x)^(k+1).

%C Columns include A016777,A003215,A096000. T(n,k)=T(n-k,k).

%F Number triangle T(n,k)=sum{j=0..n, C(k,k-j)*C(n-j,k)*C(2,j)}*[k<=n]

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 4, 1,

%e 1, 7, 7, 1,

%e 1, 10, 19, 10, 1,

%e 1, 13, 37, 37, 13, 1,

%e 1, 16, 61, 92, 61, 16, 1,

%e 1, 19, 91, 185, 185, 91, 19, 1

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Oct 28 2006