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
Examples
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
Crossrefs
Programs
-
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 */
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)).
Extensions
Edited, new name from Franck Maminirina Ramaharo, Oct 21 2018