login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 13:27 EDT 2020. Contains 335543 sequences. (Running on oeis4.)