A223529 Triangle S(n,k) by rows: coefficients of 5^((n-1)/2)*(x^(1/5)*d/dx)^n when n=1,3,5,...

1, 6, 5, 66, 110, 25, 1056, 2640, 1200, 125, 22176, 73920, 50400, 10500, 625, 576576, 2402400, 2184000, 682500, 81250, 3125, 17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625, 643458816, 3753509760, 5118422400, 2665845000, 634725000

Offset: 1

Author

Udita Katugampola, Mar 23 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
6, 5;
66, 110, 25;
1056, 2640, 1200, 125;
22176, 73920, 50400, 10500, 625;
576576, 2402400, 2184000, 682500, 81250, 3125;
17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;
643458816, 3753509760, 5118422400, 2665845000, 634725000, 73237500, 3937500, 78125;
		

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

Odd rows of A223171.

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

Programs

Maple

a[0]:= f(x):
for i from 1 to 20 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:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;