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!)
A157221 Triangle T(n, k) = Eulerian(n*f(n, k) + 1, f(n, k)), where f(n, k) = k if k <= floor(n/2) otherwise n-k, read by rows. 2
1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 14608, 26, 1, 1, 57, 152637, 152637, 57, 1, 1, 120, 1479726, 251732291184, 1479726, 120, 1, 1, 247, 13824739, 16871482830550, 16871482830550, 13824739, 247, 1, 1, 502, 126781020, 1103881308184906, 113909683214485984529600, 1103881308184906, 126781020, 502, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k) = Eulerian(n*f(n, k) + 1, f(n, k)), where f(n, k) = k if k <= floor(n/2) otherwise n-k.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 4, 1;
1, 11, 11, 1;
1, 26, 14608, 26, 1;
1, 57, 152637, 152637, 57, 1;
1, 120, 1479726, 251732291184, 1479726, 120, 1;
1, 247, 13824739, 16871482830550, 16871482830550, 13824739, 247, 1;
MATHEMATICA
f[n_, k_]:= If[k<=Floor[n/2], k, n-k];
Eulerian[n_, k_]:= Sum[(-1)^j*Binomial[n+1, j]*(k+1-j)^n, {j, 0, k+1}];
T[n_, k_]:= Eulerian[n*f[n, k] + 1, f[n, k]];
Table[Eulerian[n*f[n, k] +1, f[n, k]], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(Magma)
f:= func< n, k | k le Floor(n/2) select k else n-k >;
Eulerian:= func< n, k | (&+[(-1)^j*Binomial(n+1, j)*(k-j+1)^n: j in [0..k+1]]) >;
[Eulerian(n*f(n, k)+1, f(n, k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 10 2022
(Sage)
def f(n, k): return k if (k <= (n//2)) else n-k
def Eulerian(n, k): return sum((-1)^j*binomial(n+1, j)*(k-j+1)^n for j in (0..k+1))
flatten([[Eulerian(n*f(n, k)+1, f(n, k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jan 10 2022
CROSSREFS
Sequence in context: A174526 A008292 A174036 * A146967 A173152 A156049
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 25 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 10 2022
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 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)