A223169 - OEIS

%I #34 Dec 25 2023 18:01:42

%S 1,1,3,4,3,4,24,9,28,42,9,28,252,189,27,280,630,270,27,280,3360,3780,

%T 1080,81,3640,10920,7020,1404,81,3640,54600,81900,35100,5265,243,

%U 58240,218400,187200,56160,6480,243,58240,1048320,1965600

%N Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*d/dx)^n when n is odd, and of 3^(n/2)*(x^(2/3)*d/dx)^n when n is even.

%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 1, 3;

%e 4, 3;

%e 4, 24, 9;

%e 28, 42, 9;

%e 28, 252, 189, 27;

%e 280, 630, 270, 27;

%e 280, 3360, 3780, 1080, 81;

%e 3640, 10920, 7020, 1404, 81;

%e 3640, 54600, 81900, 35100, 5265, 243,

%e 58240, 218400, 187200, 56160, 6480, 243

%p a[0]:= f(x):

%p for i from 1 to 13 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;

%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 18 2013