%I #18 Jan 10 2024 16:00:04
%S 1,7,6,91,156,36,1729,4446,2052,216,43225,148200,102600,21600,1296,
%T 1339975,5742750,5301000,1674000,200880,7776,49579075,254978100,
%U 294205500,123876000,22297680,1726272,46656,2131900225,12791401350,17711171100,9321669000
%N Triangle S(n,k) by rows: coefficients of 6^((n-1)/2)*(x^(1/6)*d/dx)^n when n=1,3,5,...
%H U. N. Katugampola, <a href="http://authors.elsevier.com/a/1QhUNLvMg0Zs~">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, 2014
%e Triangle begins:
%e 1;
%e 7, 6;
%e 91, 156, 36;
%e 1729, 4446, 2052, 216;
%e 43225, 148200, 102600, 21600, 1296;
%e 1339975, 5742750, 5301000, 1674000, 200880, 7776;
%e 49579075, 254978100, 294205500, 123876000, 22297680, 1726272, 46656;
%e 2131900225, 12791401350, 17711171100, 9321669000, 2237200560, 259803936, 14043456, 279936;
%p a[0]:= f(x):
%p for i from 1 to 20 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:
%p for j from 1 to 10 do
%p b[j]:=a[2j-1];
%p end do;
%Y Odd rows of A223172.
%Y Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.
%K nonn,tabl
%O 1,2
%A _Udita Katugampola_, Mar 23 2013