A168292 T(n,k) = 24*A046802(n,k) - 9*A008518(n,k) - 8*A007318(n,k), triangle read by rows (0 <= k <= n).

7, 7, 7, 7, 38, 7, 7, 99, 99, 7, 7, 220, 546, 220, 7, 7, 461, 2236, 2236, 461, 7, 7, 942, 8001, 15596, 8001, 942, 7, 7, 1903, 26697, 89921, 89921, 26697, 1903, 7, 7, 3824, 85660, 463520, 796594, 463520, 85660, 3824, 7, 7, 7665, 268530, 2224350, 6068400

Offset

0,1

Links

Table of n, a(n) for n=0..49.

Formula

E.g.f.: 24*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 9*(exp(t) - x*exp(t*x))/(exp(t*x) - x*exp(t)) - 8*exp(t*(1 + x)).

Example

Triangle begins:
     7;
     7,    7;
     7,   38,     7;
     7,   99,    99,      7;
     7,  220,   546,    220,      7;
     7,  461,  2236,   2236,    461,      7;
     7,  942,  8001,  15596,   8001,    942,     7;
     7, 1903, 26697,  89921,  89921,  26697,  1903,    7;
     7, 3824, 85660, 463520, 796594, 463520, 85660, 3824, 7;
      ... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018

Prog

(Maxima)
A123125(n, k) := sum((-1)^(k - j)*(binomial(n - j, k - j))*stirling2(n, j)*j!, j, 0, k)$
A046802(n, k) := sum(binomial(n - 1, r)*A123125(r, k - 1), r, k - 1, n - 1)$
A008518(n, k) := A123125(n, k) + A123125(n, k + 1)$
T(n, k) := 24*A046802(n + 1, k + 1) - 9*A008518(n, k) - 8*binomial(n, k)$
create_list(T(n, k), n, 0, 10, k, 0, n);
/* Franck Maminirina Ramaharo, Oct 21 2018 */

Crossrefs

Triangles related to Eulerian numbers: A008292, A046802, A060187, A123125.

Cf. A142147, A142175, A168287, A168288, A168289, A168290, A168291, A168293.

Sequence in context: A337537 A003880 A084503 * A024733 A252732 A360807

Adjacent sequences: A168289 A168290 A168291 * A168293 A168294 A168295

Keyword

nonn,easy,less,tabl

Author

Roger L. Bagula, Nov 22 2009

Extensions

Edited, new name from Franck Maminirina Ramaharo, Oct 21 2018

Definition corrected by Georg Fischer, Jan 28 2026

Status

approved