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A124376
Number triangle with column k generated by x^k*(1+2kx+C(k,2)*x^2)/(1-x)^(k+1).
0
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, 1, 19, 91, 185, 185, 91, 19, 1, 1, 22, 127, 326, 440, 326, 127, 22, 1, 1, 25, 169, 525, 896, 896, 525, 169, 25, 1, 1, 28, 217, 792
OFFSET
0,5
COMMENTS
Columns include A016777,A003215,A096000. T(n,k)=T(n-k,k).
FORMULA
Number triangle T(n,k)=sum{j=0..n, C(k,k-j)*C(n-j,k)*C(2,j)}*[k<=n]
EXAMPLE
Triangle begins
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,
1, 19, 91, 185, 185, 91, 19, 1
CROSSREFS
Sequence in context: A157172 A131060 A350512 * A047671 A081577 A146986
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 28 2006
STATUS
approved