login
A number triangle of lattice walks.
1

%I #15 Mar 15 2020 04:21:22

%S 1,2,1,5,5,1,14,20,8,1,42,75,44,11,1,132,275,208,77,14,1,429,1001,910,

%T 440,119,17,1,1430,3640,3808,2244,798,170,20,1,4862,13260,15504,10659,

%U 4655,1309,230,23,1,16796,48450,62016,48279,24794,8602,2000,299,26,1

%N A number triangle of lattice walks.

%C 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.

%C Transposed version in A109450. - _Philippe Deléham_, Jun 05 2007

%H Paul Barry, <a href="https://arxiv.org/abs/1912.11845">Chebyshev moments and Riordan involutions</a>, arXiv:1912.11845 [math.CO], 2019.

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

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

%e Triangle begins

%e 1;

%e 2, 1;

%e 5, 5, 1;

%e 14, 20, 8, 1;

%e 42, 75, 44, 11, 1;

%e Triangle [1,1,1,1,1,...] DELTA [0,1,0,0,0,0,...] begins:

%e 1;

%e 1, 0;

%e 2, 1, 0;

%e 5, 5, 1, 0;

%e 14, 20, 8, 1, 0;

%e 42, 75, 44, 11, 1, 0;

%e 132, 275, 208, 77, 14, 1, 0; ...

%K easy,nonn,tabl

%O 0,2

%A _Paul Barry_, May 24 2005