The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A174298 Triangle T(n, k) = binomial(n, k)*( n!/k! if floor(n/2) >= k otherwise n!/(n-k)! ), read by rows. 1
1, 1, 1, 2, 4, 2, 6, 18, 18, 6, 24, 96, 72, 96, 24, 120, 600, 600, 600, 600, 120, 720, 4320, 5400, 2400, 5400, 4320, 720, 5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040, 40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320, 362880, 3265920, 6531840, 5080320, 1905120, 1905120, 5080320, 6531840, 3265920, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
T(n, k) = binomial(n, k)*( n!/k! if floor(n/2) >= k otherwise n!/(n-k)! ).
From G. C. Greubel, Nov 24 2021: (Start)
T(n, k) = binomial(n, k)^2*( (n-k)! if floor(n/2) >= k otherwise k! ).
T(n, 0) = T(n, n) = n!.
T(n, k) = T(n, n-k).
T(2*n, n) = (-1)^n*A295383(n). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
2, 4, 2;
6, 18, 18, 6;
24, 96, 72, 96, 24;
120, 600, 600, 600, 600, 120;
720, 4320, 5400, 2400, 5400, 4320, 720;
5040, 35280, 52920, 29400, 29400, 52920, 35280, 5040;
40320, 322560, 564480, 376320, 117600, 376320, 564480, 322560, 40320;
MATHEMATICA
T[n_, k_]:= Binomial[n, k]*If[Floor[n/2]>=k, n!/k!, n!/(n-k)!];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma)
A174298:= func< n, k | Floor(n/2) gt k select Factorial(n-k)*Binomial(n, k)^2 else Factorial(k)*Binomial(n, k)^2 >;
[A174298(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 24 2021
(Sage)
def A174298(n, k): return binomial(n, k)^2*( factorial(n-k) if ((n//2) > k-1) else factorial(k))
flatten([[A174298(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 24 2021
CROSSREFS
Cf. A295383.
Sequence in context: A138024 A167656 A253666 * A196347 A021012 A229460
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 15 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 24 2021
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 May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)