login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126454 Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 2, n-k) for n>=k>=0. 8
1, 3, 1, 15, 5, 1, 220, 55, 8, 1, 7315, 1330, 153, 12, 1, 435897, 58905, 5456, 351, 17, 1, 40475358, 4187106, 316251, 17296, 703, 23, 1, 5373200880, 437353560, 27285336, 1282975, 45760, 1275, 30, 1, 962889794295, 63140314380, 3295144749, 134153712 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
LINKS
FORMULA
T(n,k) = C( n*(n+1)*(n+2)/3! - k*(k+1)*(k+2)/3! + 2, n-k) for n>=k>=0.
EXAMPLE
Formula: T(n,k) = C( C(n+2,3) - C(k+2,3) + 2, n-k) is illustrated by:
T(n=4,k=1) = C( C(6,3) - C(3,3) + 2, n-k) = C(21,3) = 1330;
T(n=4,k=2) = C( C(6,3) - C(4,3) + 2, n-k) = C(18,2) = 153;
T(n=5,k=2) = C( C(7,3) - C(4,3) + 2, n-k) = C(33,3) = 5456.
Triangle begins:
1;
3, 1;
15, 5, 1;
220, 55, 8, 1;
7315, 1330, 153, 12, 1;
435897, 58905, 5456, 351, 17, 1;
40475358, 4187106, 316251, 17296, 703, 23, 1;
5373200880, 437353560, 27285336, 1282975, 45760, 1275, 30, 1; ...
MATHEMATICA
Table[Binomial[Binomial[n+2, 3]-Binomial[k+2, 3]+2, n-k], {n, 0, 10}, {k, 0, n}]// Flatten (* Harvey P. Dale, Dec 17 2020 *)
PROG
(PARI) T(n, k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!+2, n-k)
CROSSREFS
Columns: A126455, A126456; variants: A126445, A126450, A126457, A107870.
Sequence in context: A119301 A293157 A121335 * A293558 A259841 A228540
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Dec 27 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)