login
A168289
T(n,k) = 4*A046802(n+1,k+1) - 3*A007318(n,k), triangle read by rows (0 <= k <= n).
8
1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 48, 114, 48, 1, 1, 109, 494, 494, 109, 1, 1, 234, 1847, 3472, 1847, 234, 1, 1, 487, 6381, 20339, 20339, 6381, 487, 1, 1, 996, 21040, 107028, 179506, 107028, 21040, 996, 1, 1, 2017, 67360, 524848, 1377826, 1377826, 524848
OFFSET
0,5
FORMULA
E.g.f: 4*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 3*exp(t*(1 + x)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 6, 1;
1, 19, 19, 1;
1, 48, 114, 48, 1;
1, 109, 494, 494, 109, 1;
1, 234, 1847, 3472, 1847, 234, 1;
1, 487, 6381, 20339, 20339, 6381, 487, 1;
1, 996, 21040, 107028, 179506, 107028, 21040, 996, 1;
... reformatted. - Franck Maminirina Ramaharo, Oct 21 2018
MATHEMATICA
p[t_] = 4*(1 - x)*Exp[t]/(1 - x*Exp[t*(1 - x)]) - 3*Exp[t*(1 + x)];
Table[CoefficientList[FullSimplify[n!*SeriesCoefficient[Series[p[t], {t, 0, n}], n]], x], {n, 0, 10}]//Flatten
PROG
(Maxima)
A046802(n, k) := sum(binomial(n - 1, r)*sum(j!*(-1)^(k - j - 1)*stirling2(r, j)*binomial(r - j, k - j - 1), j, 0, k - 1), r, k - 1, n - 1)$
T(n, k) := 4*A046802(n + 1, k + 1) - 3*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.
Sequence in context: A157632 A328888 A176125 * A141690 A318408 A146957
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, Nov 22 2009
EXTENSIONS
Edited, and new name by Franck Maminirina Ramaharo, Oct 21 2018
STATUS
approved