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A223525 Triangle S(n,k) by rows: coefficients of 3^((n-1)/2))*(x^(1/3)*d/dx)^n when n=1,3,5,... 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..37.

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;

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;

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;

CROSSREFS

Odd rows of A223169.

Cf. A223168-A223172, A223511-A223532.

Sequence in context: A074296 A085961 A175325 * A205446 A343919 A152191

Adjacent sequences:  A223522 A223523 A223524 * A223526 A223527 A223528

KEYWORD

nonn,tabl

AUTHOR

Udita Katugampola, Mar 18 2013

STATUS

approved

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Last modified August 2 08:00 EDT 2021. Contains 346422 sequences. (Running on oeis4.)