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URL: https://oeis.org/A107842

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A107842
A number triangle of lattice walks.
1
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
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: A123971 A060920 A391610 * A126216 A124733 A137597
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, May 24 2005
STATUS
approved