A223171 Triangle S(n,k) by rows: coefficients of 5^((n-1)/2)*(x^(1/5)*d/dx)^n when n is odd, and of 5^(n/2)*(x^(4/5)*d/dx)^n when n is even.

1, 1, 5, 6, 5, 6, 60, 25, 66, 110, 25, 66, 990, 825, 125, 1056, 2640, 1200, 125, 1056, 21120, 26400, 8000, 625, 22176, 73920, 50400, 10500, 625, 22176, 554400, 924000, 420000, 65625, 3125, 576576, 2402400, 2184000, 682500, 81250, 3125, 576576, 17297280

Offset: 0

Author

Udita Katugampola, Mar 20 2013

Keywords

• nonn
• tabf

Examples

			Triangle begins:
1;
1, 5;
6, 5;
6, 60, 25;
66, 110, 25;
66, 990, 825, 125;
1056, 2640, 1200, 125;
1056, 21120, 26400, 8000, 625;
22176, 73920, 50400, 10500, 625;
22176, 554400, 924000, 420000, 65625, 3125;
576576, 2402400, 2184000, 682500, 81250, 3125;
576576, 17297280, 36036000, 21840000, 5118750, 487500, 15625;
17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;
		

Links

• U. N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257(2015) 566-580.
• U. N. Katugampola, Existence and Uniqueness results for a class of Generalized Fractional Differential Equations, arXiv preprint arXiv:1411.5229, 2014

Crossrefs

Cf. A223168-A223172, A223523-A223532, A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522.

Programs

Maple

a[0]:= f(x):
for i from 1 to 13 do
a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(diff(a[i-1],x$1 )));
end do;