A124376 Number triangle with column k generated by x^k*(1+2kx+C(k,2)*x^2)/(1-x)^(k+1).

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).

Links

Table of n, a(n) for n=0..58.

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

Adjacent sequences: A124373 A124374 A124375 * A124377 A124378 A124379

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 28 2006

Status

approved