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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122176 Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 1, n-k) for n>=k>=0. 6
1, 2, 1, 3, 3, 1, 4, 6, 5, 1, 5, 10, 15, 8, 1, 6, 15, 35, 36, 12, 1, 7, 21, 70, 120, 78, 17, 1, 8, 28, 126, 330, 364, 153, 23, 1, 9, 36, 210, 792, 1365, 969, 276, 30, 1, 10, 45, 330, 1716, 4368, 4845, 2300, 465, 38, 1, 11, 55, 495, 3432, 12376, 20349, 14950, 4960, 741, 47, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Remarkably, column k of the matrix inverse (A121436) equals signed column k of matrix power: A107876^(k*(k+1)/2 + 2).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..10000

EXAMPLE

Triangle begins:

1;

2, 1;

3, 3, 1;

4, 6, 5, 1;

5, 10, 15, 8, 1;

6, 15, 35, 36, 12, 1;

7, 21, 70, 120, 78, 17, 1;

8, 28, 126, 330, 364, 153, 23, 1;

9, 36, 210, 792, 1365, 969, 276, 30, 1; ...

MATHEMATICA

Flatten[Table[Binomial[(k(k+1))/2+n-k+1, n-k], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Mar 18 2013 *)

PROG

(PARI) T(n, k)=if(n<k|k<0, 0, binomial(k*(k+1)/2+n-k+1, n-k))

CROSSREFS

Cf. A121436 (inverse); variants: A098568, A122175, A122177.

Sequence in context: A323346 A143328 A192001 * A159881 A319539 A098546

Adjacent sequences:  A122173 A122174 A122175 * A122177 A122178 A122179

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Aug 25 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 November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)