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%I #22 Jan 10 2024 15:59:13
%S 1,4,3,4,24,9,28,252,189,27,280,3360,3780,1080,81,3640,54600,81900,
%T 35100,5265,243,1106560,4979520,5335200,2134080,369360,27702,729,
%U 24344320,127807680,164324160,82162080,18960480,2133054,112266,2187,608608000
%N Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*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 4, 3;
%e 4, 24, 9;,
%e 28, 252, 189, 27;
%e 280, 3360, 3780, 1080, 81;
%e 3640, 54600, 81900, 35100, 5265, 243;
%e 1106560, 4979520, 5335200, 2134080, 369360, 27702, 729;
%e 24344320, 127807680, 164324160, 82162080, 18960480, 2133054, 112266, 2187;
%p a[0]:= f(x):
%p for i from 1 to 20 do
%p a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(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 A223169.
%Y Cf. A223168-A223172, A223511-A223532.
%K nonn,tabl
%O 1,2
%A _Udita Katugampola_, Mar 18 2013
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