%I #37 Dec 25 2023 18:02:50
%S 1,1,6,7,6,7,84,36,91,156,36,91,1638,1404,216,1729,4446,2052,216,1729,
%T 41496,53352,16416,1296,43225,148200,102600,21600,1296,43225,1296750,
%U 2223000,1026000,162000,7776,1339975,5742750,5301000,1674000,200880,7776
%N Triangle S(n,k) by rows: coefficients of 6^((n-1)/2)*(x^(1/6)*d/dx)^n when n is odd, and of 6^(n/2)*(x^(5/6)*d/dx)^n when n is even.
%H U. N. Katugampola, <a href="http://dx.doi.org/10.1016/j.amc.2014.12.067">Mellin Transforms of Generalized Fractional Integrals and Derivatives</a>, Appl. Math. Comput. 257(2015) 566-580.
%H U. N. Katugampola, <a href="http://arxiv.org/abs/1411.5229">Existence and Uniqueness results for a class of Generalized Fractional Differential Equations</a>, arXiv preprint arXiv:1411.5229 [math.CA], 2014.
%e Triangle begins:
%e 1;
%e 1, 6;
%e 7, 6;
%e 7, 84, 36;
%e 91, 156, 36;
%e 91, 1638, 1404, 216;
%e 1729, 4446, 2052, 216;
%e 1729, 41496, 53352, 16416, 1296;
%e 43225, 148200, 102600, 21600, 1296;
%e 43225, 1296750, 2223000, 1026000, 162000, 7776;
%e 1339975, 5742750, 5301000, 1674000, 200880, 7776;
%e 1339975, 48239100, 103369500, 63612000, 15066000, 1446336, 46656;
%p a[0]:= f(x):
%p for i from 1 to 13 do
%p a[i] := simplify(6^((i+1)mod 2)*x^((4((i+1)mod 2)+1)/6)*(diff(a[i-1],x$1 )));
%p end do;
%Y Cf. A223168-A223172, A223523-A223532, A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522.
%K nonn,tabf
%O 0,3
%A _Udita Katugampola_, Mar 20 2013