A168292 T(n,k) = 24*A046802(n+1,k+1) - 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

Status

approved