A223525 Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*d/dx)^n when n=1,3,5,...

1, 4, 3, 4, 24, 9, 28, 252, 189, 27, 280, 3360, 3780, 1080, 81, 3640, 54600, 81900, 35100, 5265, 243, 1106560, 4979520, 5335200, 2134080, 369360, 27702, 729, 24344320, 127807680, 164324160, 82162080, 18960480, 2133054, 112266, 2187, 608608000

Offset: 1

Author

Udita Katugampola, Mar 18 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
4, 3;
4, 24, 9;,
28, 252, 189, 27;
280, 3360, 3780, 1080, 81;
3640, 54600, 81900, 35100, 5265, 243;
1106560, 4979520, 5335200, 2134080, 369360, 27702, 729;
24344320, 127807680, 164324160, 82162080, 18960480, 2133054, 112266, 2187;
		

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 A223169.

Cf. A223168-A223172, A223511-A223532.

Programs

Maple

a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1],x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;