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

1,3

Links

Table of n, a(n) for n=1..39.

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

Formula

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

Example

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;

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;

Crossrefs

Even row of A223169.

Cf. A223168-A223172, A223511-A223532.

Sequence in context: A041861 A042377 A276815 * A032831 A047180 A051394

Adjacent sequences: A223523 A223524 A223525 * A223527 A223528 A223529

Keyword

nonn,tabl

Author

Udita Katugampola, Mar 18 2013

Status

approved