A223529 - OEIS

%I #20 Jan 10 2024 15:59:50

%S 1,6,5,66,110,25,1056,2640,1200,125,22176,73920,50400,10500,625,

%T 576576,2402400,2184000,682500,81250,3125,17873856,89369280,101556000,

%U 42315000,7556250,581250,15625,643458816,3753509760,5118422400,2665845000,634725000

%N Triangle S(n,k) by rows: coefficients of 5^((n-1)/2)*(x^(1/5)*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 6, 5;

%e 66, 110, 25;

%e 1056, 2640, 1200, 125;

%e 22176, 73920, 50400, 10500, 625;

%e 576576, 2402400, 2184000, 682500, 81250, 3125;

%e 17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;

%e 643458816, 3753509760, 5118422400, 2665845000, 634725000, 73237500, 3937500, 78125;

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

%p for i from 1 to 20 do

%p a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(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 A223171.

%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