A107027 Number triangle associated to the Riordan arrays (1/(1+x),x/(1+x)^k),k>=0.

1, 1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 6, 8, 2, 1, 2, 8, 20, 16, 2, 1, 2, 10, 38, 70, 32, 2, 1, 2, 12, 62, 196, 252, 64, 2, 1, 2, 14, 92, 426, 1062, 924, 128, 2, 1, 2, 16, 128, 792, 3112, 5948, 3432, 256, 2, 1, 2, 18, 170, 1326, 7302, 23686, 34120, 12870, 512, 2, 1, 2, 20, 218

Offset

0,3

Comments

As a number square read by antidiagonals, the rows represent the row sums of the inverses of the Riordan arrays (1/(1+x),x/(1+x)^k), k>=0. The rows are then given by T(n,k)=(n-1)C(n*k,k)-(n-2)*sum{j=0..k, C(n*k,j)}. T(n,n) is A040000, T(n+1,n) is A000079, T(n+2,n) is A000984, T(n+3,n) is A047098. The reverse of this triangle is A107030. Row sums are A107028. Diagonal sums are A107029.

Links

Table of n, a(n) for n=0..69.

Formula

Number triangle T(n, k)=if(k<=n, (n-k-1)C((n-k)*k, k)-(n-k-2)*sum{j=0..k, C((n-k)*k, j)}, 0).

Example

Triangle begins
1;
1,2;
1,2,2;
1,2,4,2;
1,2,6,8,2;
1,2,8,20,16,2;

Crossrefs

Sequence in context: A178522 A131240 A263666 * A355395 A107030 A371692

Adjacent sequences: A107024 A107025 A107026 * A107028 A107029 A107030

Keyword

easy,nonn,tabl

Author

Paul Barry, May 09 2005

Status

approved