A223526 Triangle S(n,k) by rows: coefficients of 3^(n/2)*(x^(2/3)*d/dx)^n when n=0,2,4,6,...

1, 1, 3, 4, 24, 9, 28, 252, 189, 27, 280, 3360, 3780, 1080, 81, 3640, 54600, 81900, 35100, 5265, 243, 58240, 1048320, 1965600, 1123200, 252720, 23328, 729, 1106560, 23237760, 52284960, 37346400, 11203920, 1551312, 96957, 2187, 24344320, 584263680, 1533692160

Offset: 1

Author

Udita Katugampola, Mar 18 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
1, 3;
4, 24, 9;
28, 252, 189, 27;
280, 3360, 3780, 1080, 81;
3640, 54600, 81900, 35100, 5265, 243;
58240, 1048320, 1965600, 1123200, 252720, 23328, 729;
1106560, 23237760, 52284960, 37346400, 11203920, 1551312, 96957, 2187;
24344320, 584263680, 1533692160, 1314593280, 492972480, 91010304, 8532216, 384912, 6561;
		

Links

• U. N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257(2015) 566-580.

Crossrefs

Even row 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];
end do;

Formula

T(n,0) = A007559(n) and T(n,n) = A000244(n) for all n>=0