OFFSET
0,5
FORMULA
E.g.f.: 4*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 2*(exp(t) - x*exp(t*x))/(exp(t*x) - x*exp(t)) - exp(t*(1 + x)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 6, 1;
1, 15, 15, 1;
1, 32, 82, 32, 1;
1, 65, 330, 330, 65, 1;
1, 130, 1159, 2304, 1159, 130, 1;
1, 259, 3801, 13195, 13195, 3801, 259, 1;
1, 516, 12016, 67316, 117170, 67316, 12016, 516, 1;
... 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)$
create_list(T(n, k), n, 0, 10, k, 0, n);
/* Franck Maminirina Ramaharo, Oct 21 2018 */
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Nov 22 2009
EXTENSIONS
Edited, new name by Franck Maminirina Ramaharo, Oct 21 2018
STATUS
approved