login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110488 A number triangle based on the Catalan numbers. 3
1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 14, 14, 10, 4, 1, 42, 42, 35, 17, 5, 1, 132, 132, 126, 74, 26, 6, 1, 429, 429, 462, 326, 137, 37, 7, 1, 1430, 1430, 1716, 1446, 726, 230, 50, 8, 1, 4862, 4862, 6435, 6441, 3858, 1434, 359, 65, 9, 1, 16796, 16796, 24310, 28770, 20532, 8952, 2582, 530, 82, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Columns include A000108, A001700, A049027(n+1), A076025(n+1). Rows sums are A110489, diagonal sums are A110490.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(n, k) = Sum_{j=0..(n-k)} 2*(j+1)*(k-1)^j*C(2(n-k)+1, n-k-j)/(n-k+j+2)}.

Column k has g.f. x^k*c(x)/(1-k*x*c(x)) where c(x) is the g.f. of A000108.

T(n,0) = Catalan(n), T(n,1) = Catalan(n), T(n,n) = 1. - G. C. Greubel, Aug 28 2017

EXAMPLE

Rows begin

   1;

   1,  1;

   2,  2,  1;

   5,  5,  3,  1;

  14, 14, 10,  4,  1;

  42, 42, 35, 17,  5,  1;

MATHEMATICA

T[n_, 0] := CatalanNumber[n]; T[n_, 1] := CatalanNumber[n]; T[n_, n_] := 1; T[n_, k_] := Sum[2*(j + 1)*(k - 1)^j*Binomial[2 (n - k) + 1, n - k - j]/(n - k + j + 2), {j, 0, n - k}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 28 2017 *)

CROSSREFS

Sequence in context: A079222 A033184 A171567 * A271025 A134379 A108087

Adjacent sequences:  A110485 A110486 A110487 * A110489 A110490 A110491

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jul 22 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 19 03:29 EST 2018. Contains 299330 sequences. (Running on oeis4.)