A109450 -id:A109450 - cp's OEIS frontend

A107842 A number triangle of lattice walks.

1, 2, 1, 5, 5, 1, 14, 20, 8, 1, 42, 75, 44, 11, 1, 132, 275, 208, 77, 14, 1, 429, 1001, 910, 440, 119, 17, 1, 1430, 3640, 3808, 2244, 798, 170, 20, 1, 4862, 13260, 15504, 10659, 4655, 1309, 230, 23, 1, 16796, 48450, 62016, 48279, 24794, 8602, 2000, 299, 26, 1

Offset: 0

Paul Barry, May 24 2005

First column is A000108(n+1). Columns include A000344, A003518 and A000589. Row sums are A026671. Compare [1,1,1,...] DELTA [0,1,0,0,...] where DELTA is the operator defined in A084938.

Transposed version in A109450. - Philippe Deléham, Jun 05 2007

			Triangle begins
   1;
   2,  1;
   5,  5,  1;
  14, 20,  8,  1;
  42, 75, 44, 11,  1;
Triangle [1,1,1,1,1,...] DELTA [0,1,0,0,0,0,...] begins:
    1;
    1,   0;
    2,   1,   0;
    5,   5,   1,   0;
   14,  20,   8,   1,   0;
   42,  75,  44,  11,   1,   0;
  132, 275, 208,  77,  14,   1,   0; ...

Paul Barry, Chebyshev moments and Riordan involutions, arXiv:1912.11845 [math.CO], 2019.

Number triangle T(n, k) = (3k+2)*C(2n+k+1, n-k)/(n+2k+2).

Column k has g.f.: x^k*C(x)^(3k+2) where C(x) is the g.f. of A000108.

cp's OEIS Frontend

A107842 A number triangle of lattice walks.

Views

Author

Keywords

Comments

Examples

Links

Formula