A124445 Expansion of 1/(1-x-x*y+x^2*y-x^3*y^2).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 5, 4, 1, 1, 1, 5, 7, 8, 5, 1, 1, 1, 6, 9, 13, 12, 6, 1, 1, 1, 7, 11, 19, 22, 17, 7, 1, 1, 1, 8, 13, 26, 35, 35, 23, 8, 1, 1, 1, 9, 15, 34, 51, 61, 53, 30, 9, 1

Offset

0,9

Comments

Row sums are A107293(n+4). Diagonal sums are A005314(n+1).

Reversal of A124279. T(2n,n) is A002426. - Paul Barry, Nov 01 2006

Links

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

Formula

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

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,0) = T(1,1) = T(2,0) = T(2,1) = T(2,2) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 25 2014

Example

Triangle begins:
1,
1, 1,
1, 1, 1,
1, 1, 2, 1,
1, 1, 3, 3, 1,
1, 1, 4, 5, 4, 1,
1, 1, 5, 7, 8, 5, 1,
1, 1, 6, 9, 13, 12, 6, 1,
1, 1, 7, 11, 19, 22, 17, 7, 1

Crossrefs

Cf. A180562.

Sequence in context: A254055 A096815 A193516 * A124279 A297299 A135225

Adjacent sequences: A124442 A124443 A124444 * A124446 A124447 A124448

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 01 2006

Status

approved