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

0,2

Comments

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

Links

Table of n, a(n) for n=0..54.

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

Formula

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.

Example

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; ...

Crossrefs

Sequence in context: A126124 A123971 A060920 * A126216 A124733 A137597

Adjacent sequences: A107839 A107840 A107841 * A107843 A107844 A107845

Keyword

easy,nonn,tabl

Author

Paul Barry, May 24 2005

Status

approved