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!)
A115253 "Correlation triangle" for Catalan numbers. 2
1, 1, 1, 2, 2, 2, 5, 3, 3, 5, 14, 7, 6, 7, 14, 42, 19, 13, 13, 19, 42, 132, 56, 35, 31, 35, 56, 132, 429, 174, 103, 83, 83, 103, 174, 429, 1430, 561, 320, 245, 227, 245, 320, 561, 1430, 4862, 1859, 1032, 763, 671, 671, 763, 1032, 1859, 4862, 16796, 6292, 3421 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A094639. Diagonal sums are A115254. Corresponds to the triangle of antidiagonals of the correlation matrix of the sequence array for C(n).

LINKS

Table of n, a(n) for n=0..57.

FORMULA

G.f.: c(x)c(x*y)/(1-x^2*y) where c(x) is the g.f. of A000108 (format due to Christian G. Bower).

T(n, k) = sum{j=0..n, [j<=k]*C(k-j)[j<=n-k]*C(n-k-j)}.

O.g.f.: F(z,v) = 1/4 ((1-sqrt(1-4 z)) (1-sqrt(-4 v z+1)))/(z^2 v (-v z^2+1)). - Yu-Sheng Chang, Jun 12 2020

EXAMPLE

Triangle begins

1;

1, 1;

2, 2, 2;

5, 3, 3, 5;

14, 7, 6, 7, 14;

42, 19, 13, 13, 19, 42;

CROSSREFS

Sequence in context: A061311 A174960 A210239 * A154429 A333388 A174577

Adjacent sequences:  A115250 A115251 A115252 * A115254 A115255 A115256

KEYWORD

easy,nonn,tabl,changed

AUTHOR

Paul Barry, Jan 18 2006

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 12 02:34 EDT 2020. Contains 335658 sequences. (Running on oeis4.)