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A223529 Triangle S(n,k) by rows: coefficients of 5^((n-1)/2))*(x^(1/5)*d/dx)^n when n=1,3,5,... 0
1, 6, 5, 66, 110, 25, 1056, 2640, 1200, 125, 22176, 73920, 50400, 10500, 625, 576576, 2402400, 2184000, 682500, 81250, 3125, 17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625, 643458816, 3753509760, 5118422400, 2665845000, 634725000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..33.

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;

6, 5;

66, 110, 25;

1056, 2640, 1200, 125;

22176, 73920, 50400, 10500, 625;

576576, 2402400, 2184000, 682500, 81250, 3125;

17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;

643458816, 3753509760, 5118422400, 2665845000, 634725000, 73237500, 3937500, 78125;

MAPLE

a[0]:= f(x):

for i from 1 to 20 do

a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(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 A223171.

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

Sequence in context: A038259 A302750 A268000 * A189422 A266980 A130554

Adjacent sequences:  A223526 A223527 A223528 * A223530 A223531 A223532

KEYWORD

nonn,tabl

AUTHOR

Udita Katugampola, Mar 23 2013

STATUS

approved

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Last modified August 2 06:52 EDT 2021. Contains 346411 sequences. (Running on oeis4.)