A188316 Riordan array (1/(1-x^2), x/((1-x)*(1-x^2))).

1, 0, 1, 1, 1, 1, 0, 3, 2, 1, 1, 3, 6, 3, 1, 0, 6, 10, 10, 4, 1, 1, 6, 20, 22, 15, 5, 1, 0, 10, 30, 49, 40, 21, 6, 1, 1, 10, 50, 91, 100, 65, 28, 7, 1, 0, 15, 70, 168, 216, 181, 98, 36, 8, 1, 1, 15, 105, 280, 444, 441, 301, 140, 45, 9, 1

Offset

0,8

Comments

Row sums are A077998.

Diagonal sums are A052547.

Inverse is A188317.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) - T(n-3,k), T(0,0) = T(1,1) = T(2,0) = T(2,1) = T(2,2)=1, T(1,0)=0, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 16 2014

Example

Triangle begins
1,
0, 1,
1, 1, 1,
0, 3, 2, 1,
1, 3, 6, 3, 1,
0, 6, 10, 10, 4, 1,
1, 6, 20, 22, 15, 5, 1,
0, 10, 30, 49, 40, 21, 6, 1,
1, 10, 50, 91, 100, 65, 28, 7, 1,
0, 15, 70, 168, 216, 181, 98, 36, 8, 1

Crossrefs

Sequence in context: A321620 A353157 A134520 * A197027 A143772 A053989

Adjacent sequences: A188313 A188314 A188315 * A188317 A188318 A188319

Keyword

nonn,tabl

Author

Paul Barry, Mar 28 2011

Status

approved