A223169 - OEIS

A223169

Triangle S(n,k) by rows: coefficients of 3^((n-1)/2)*(x^(1/3)*d/dx)^n when n is odd, and of 3^(n/2)*(x^(2/3)*d/dx)^n when n is even.

1, 1, 3, 4, 3, 4, 24, 9, 28, 42, 9, 28, 252, 189, 27, 280, 630, 270, 27, 280, 3360, 3780, 1080, 81, 3640, 10920, 7020, 1404, 81, 3640, 54600, 81900, 35100, 5265, 243, 58240, 218400, 187200, 56160, 6480, 243, 58240, 1048320, 1965600

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..43.

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

EXAMPLE

Triangle begins:

1, 3;

4, 3;

4, 24, 9;

28, 42, 9;

28, 252, 189, 27;

280, 630, 270, 27;

280, 3360, 3780, 1080, 81;

3640, 10920, 7020, 1404, 81;

3640, 54600, 81900, 35100, 5265, 243,

58240, 218400, 187200, 56160, 6480, 243

MAPLE

a[0]:= f(x):

for i from 1 to 13 do

a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1], x$1 )));

end do;

CROSSREFS

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

Sequence in context: A265305 A072942 A025267 * A201420 A244055 A090739

Adjacent sequences: A223166 A223167 A223168 * A223170 A223171 A223172

KEYWORD

nonn,tabf

AUTHOR

Udita Katugampola, Mar 18 2013

STATUS

approved