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!)
A155825 Triangle T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k), read by rows. 1
1, 0, 0, 0, 1, 0, 0, 12, 12, 0, 0, 216, 484, 216, 0, 0, 5760, 21000, 21000, 5760, 0, 0, 216000, 1117920, 1822500, 1117920, 216000, 0, 0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0, 0, 711244800, 6059370240, 18531878400, 26391951936, 18531878400, 6059370240, 711244800, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
FORMULA
T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k).
EXAMPLE
Triangle begins as:
1;
0, 0;
0, 1, 0;
0, 12, 12, 0;
0, 216, 484, 216, 0;
0, 5760, 21000, 21000, 5760, 0;
0, 216000, 1117920, 1822500, 1117920, 216000, 0;
0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0;
MATHEMATICA
T[n_, k_]:= (-1)^n*n!*StirlingS1[n, k]StirlingS1[n, n-k]/Binomial[n, k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma) [(-1)^n*Factorial(n)*StirlingFirst(n, k)*StirlingFirst(n, n-k)/Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 03 2021
(Sage) flatten([[factorial(n)*stirling_number1(n, k)*stirling_number1(n, n-k)/binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 03 2021
CROSSREFS
Cf. A048994.
Sequence in context: A254717 A195748 A038337 * A125509 A281251 A247511
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 28 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 03 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 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)